partial derivatives pdf

Likewise, for and . If z = f(x,y) = x4y3 +8x2y +y4 +5x, then the partial derivatives are ∂z ∂x = 4x3y3 +16xy +5 (Note: y ﬁxed, x independent variable, z … This Study Material on Partial Differentiation can be downloaded in PDF so that your preparation is made easy. The tangent line to the curve at P is the line in the plane y = y 0 that passes through P with this slope. ft(x,t)=e tcos(⇡x) 109 of 139. It turns that this will usually be the case. We differentiate one of the variables while keeping the other variable fixed. The gradient. Here are some basic examples: 1. stream Get Daily GK & Current Affairs Capsule & PDFs, Sign Up for Free Create free Account? This way we had two different derivatives and to distinguish them one is … If f(x,y) is a function of two variables, then ∂f ∂x and ∂f ∂y are also functions of two variables and their partials can be taken. Partial derivative and gradient (articles) Introduction to partial derivatives. Don't show me this again. << /S /GoTo /D (subsection.3.4) >> These GATE 2019 Notes are important for GATE EC, GATE EE, GATE ME, GATE CE, GATE CS as well as for other exams like IES, BARC, BSNL, DRDO etc. (Chain Rule) Functions of Several Variables Level Curves Partial Derivatives Maxima and Minima of Functions of Several Variables Constrained Maxima and Minima and the … We will give the formal definition of the partial derivative as well as the standard notations and how to compute them in practice (i.e. This is the currently selected item. << /S /GoTo /D (subsection.3.2) >> Partial Derivatives The derivative of a function, f(x), of one variable tells you how quickly f(x) changes as you increase the value of the variable x. Our mission is to provide a free, world-class … Second partial derivatives. Before you start, get basics in Engineering Mathematics right. Welcome! 4. endobj f xxx= @3f @x3 = @ @x @2f @x2 ; f xyy = @3f @y2@x = @ @y @2f @y@x f xyxz = @4f @z@x@y@x = @ @z @3f @x@y@x For … We do this by placing 1. subscripts on our partial derivatives. x,z dy + ∂w … All other variables are treated as constants. You may also like the following articles –, Recommended Books for Engineering MathematicsList of 40+ PSUs Recruiting through GATE 2019, For more information on GATE 2019, you can click the links given below –. You just have to remember with which variable you are taking the derivative. So, we can just plug that in ahead of time. Directional derivatives (introduction) Directional derivatives (going deeper) Next lesson. Explanation: the derivative of x 2 (with respect to x) is 2x; we treat y as a constant, so y 3 is also a constant (imagine y=7, then 7 3 =343 is also a constant), and the derivative of a constant is 0; To find the partial derivative with respect to y, we treat x as a constant: f’ y = 0 + 3y 2 = … A short summary of this paper. And I'll say X … For example, given the equations y = a+bx or y = axn we automatically treated a, b,andn as constants and took the derivative of y with respect to x (dy/dx). 13 0 obj 11 Partial derivatives and multivariable chain rule 11.1 Basic deﬁntions and the Increment Theorem One thing I would like to point out is that you’ve been taking partial derivatives all your calculus-life. Higher-order partial derivatives that are taken with respect to different variables, such as $\dfrac{∂^2f}{∂y∂x}$ and $\dfrac{∂^2f}{∂x∂y}$, are called mixed partial derivatives. Don't show me this again. The partial derivative @f =@x at (x 0;y 0) … Find the ﬁrst partial derivatives of the function f(x,t)=e t cos(⇡x) Since there is only two variables, there are two ﬁrst partial derivatives. << /S /GoTo /D (subsection.3.3) >> So, I'm gonna say partial, partial X, this is another way you might write it, put the expression in here. Partial derivatives are computed similarly to the two variable case. Delhi Police Constable Exam Analysis Shift 1 27 Nov 2020 Out – Get First Shift Analysis Here! Thus we can rewrite our expression for the diﬀerential of w as dw = ∂w ∂x! View partial derivative 2.pdf from MATHS 123 at Nirma University, Ahmedabad. Section 1: Partial Diﬀerentiation (Introduction) 3 1. Partial derivative of F, with respect to X, and we're doing it at one, two. No … (20) We would like to transform to polar co-ordinates. We have learnt Differentiation in last topic. Let us know in the comments? If z = f(x,y) then the partial derivatives ∂f ∂x and ∂f ∂y can be interpreted as the gradients of the tangent lines to the surface z = f(x,y) in the directions parallel to the x− and y−axes, respectively. Differentiating parametric curves. Here is an excerpt of the article. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. (Higher Order Partial Derivatives) Notice in the above example that $\dfrac{∂^2f}{∂y∂x} = \dfrac{∂^2f}{∂x∂y}$. Partial Derivatives Examples And A Quick Review of Implicit Diﬀerentiation Given a multi-variable function, we deﬁned the partial derivative of one variable with respect to another variable in class. It is denoted ∂f ∂x (x,y) and tells you how quickly f(x,y) changes as you increase the value of the variable x while holding the value of the … IBPS SO Prelims Exam Analysis 2020 – All Shifts 26th December 2020, RPSC JLO Result 2020 Declared – Direct Link to Check Result & Interview Dates, BSSC Rajbhasha Sahayak Admit Card 2020 – Direct Link To Download @bssc.bih.nic.in. Suppose, we have a function f(x,y), which depends on two variables x and y, where x and y are independent of each other. Partial Diﬀerentiation 14.1 Functions of l Severa riables a V In single-variable calculus we were concerned with functions that map the real numbers R to R, sometimes called “real functions of one variable”, meaning the “input” is a single real number and the “output” is likewise a single real number. † @ 2z @x2 means the second derivative with respect to x … A partial di erential equation is an equation for a function which depends on more than one independent variable which involves the independent variables, the function, and partial derivatives of the function: there are three partial derivatives: f x, f y and f z The partial derivative is calculate d by holding y and z constant. Partial Derivatives.pdf - Calculus of Several Variables... School Punjab University College Of Information Technology; Course Title PUCIT CS-310; Uploaded By ChiefMousePerson157. %PDF-1.4 As far as it's concerned, Y is always equal to two. /Filter /FlateDecode Our team is there to help you all the time. To find its partial derivative with respect to x we treat y as a constant (imagine y is a number like 7 or something): f ’ x = 2x + 0 = 2x. 23 Full PDFs related to this paper. Note that a function of three variables does not have a graph. Hence we can diﬀerentiate them with respect to x and y again and ﬁnd, ∂2f ∂x2, the derivative of f taken twice with respect to x, ∂2f ∂x∂y, … OK, so most of the functions we'll see are differentiable. Higher-order derivatives Third-order, fourth-order, and higher-order derivatives are obtained by successive di erentiation. Specifically, whenever both $\dfrac{∂^2f}{∂y∂x}$ and $\dfrac{∂^2f}{∂x∂y}$ are continuous at a point … So, this time I keep x the same, but I change y. OK, so that's the definition of a partial derivative. y,z dx+ ∂w ∂y! Here, x is ﬁxed so cos(⇡x) is just a constant. Learn more about livescript In this module we will always assume that derivatives exist unless it is otherwise stated. Bihar Police Driver Constable Test Series, GATE (Graduate Aptitude Test in Engineering). Relationships between Partial Derivatives We can use the deﬁnition of the total diﬀerential to develop relationships between partial derivatives. Partial f partial y is the limit, so I should say, at a point x0 y0 is the limit as delta y turns to zero. So, et is just a constant. It is called partial derivative of f with respect to x. In other words the variable value f(x, y) approaches finite fixed value l in the codomain when the variable value (x, y) approaches a fixed value (a, b) i.e. Partial Derivatives Single variable calculus is really just a ”special case” of multivariable calculus. Now let’s take a look at another concept in Calculus – Partial Differentiation. Partial Diﬀerentiation (Introduction) In the package on introductory diﬀerentiation, rates of change of … Nevertheless, recall that to calculate a partial derivative of a function with respect to a specified variable, just find the ordinary derivative of the function while treating the other variables as constants. Now let’s take a look at another concept in Calculus – Partial Differentiation. Sort by: Top Voted. Evaluate your performance & work on your weak areas. Testbook GATE FEST 2021 – Check your Knowledge & Win! For the function y = f(x), we assumed that y was the endogenous variable, x was the exogenous variable and everything else was a parameter. 16 0 obj Equality of mixed partial derivatives Theorem. The notation df /dt tells you that t is the variables and everything else you see is a constant. endobj Lecture 9: Partial derivatives If f(x,y) is a function of two variables, then ∂ ∂x f(x,y) is deﬁned as the derivative of the function g(x) = f(x,y), where y is considered a constant. It doesn't even care about the fact that Y changes. If we use the notation f0 instead, then … As these examples show, calculating a partial derivatives is usually just like calculating an ordinary derivative of one-variable calculus. Like ordinary derivatives, partial derivatives do not always exist at every point. Did you like this article on Partial Differentiation? It only cares about movement in the X direction, so it's treating Y as a constant. In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Higher Order Partial Derivatives 4. Discuss the applications of partial derivatives in daily life with at least 2 examples. There is only one (very important) subtlety that you need to … x��YK��6��W�(#�"�d�䰛�6�C&Ŗ�º��nO��|EJj�M?f�Ӌ݋M��b��Ջ��f��Li+��E&g�h�Y��f7��rŦ��%~�4�� }}X֛i�J��s3��'|��y��]��Vq��H��V�ծkcB�N��;a ��xVHɄ�>��"I?&B�q�@L4�4��-DR&��⾝��T�m�X/��~��2�7�V��aj0q�P��(�*��㳟JG[S��{.t;��e�a�F*T:_C�]��R��g��qq?�W�|Gl$^�fV�5I�o�q�6��vK��E=i�\�`͝ ��6��xn �$��sG��N�;��qm��z� O��?~ �l�?&O�1�0y�'R�{f�DCwU�� /B��kj��"m6�@P�:�DWQ��%Aϣ�&Mwx�N�"&?�LH3��lf��|#��o��l>��t�d��gRy��N. partial derivative coding in matlab . Problems: Partial Derivatives (PDF) Solutions (PDF) « Previous | Next » Need help getting started? However, what if … In the last chapter we considered functions taking a real number to a vector, which may also be viewed … First, let’s consider fx. De nition: lim (x;y)! Multivariate Calculus; Fall 2013 S. Jamshidi Example 5.3.0.5 2. x approaches a and y approaches b simultaneously. Once you understand the concept of a partial derivative as the rate that something is changing, calculating partial derivatives usually isn't difficult. This paper. … The technique of differentiating multivariable function is known as Partial Differentiation and the resulting derivative is called Partial Derivative. These GATE 2019 Notes are important for GATE EC, GATE EE, GATE ME, GATE CE, GATE CS as well as for other exams like IES, BARC, BSNL, DRDO etc. … 8 0 obj For a function f(x,y) of two variables, there are two corresponding derivatives. Partial Derivatives of a Function of Two Variables An equivalent expression for the partial derivative is d dx f (x;y 0) x=x0: The slope of the curve z = f (x;y 0) at the point P(x 0;y 0;f (x 0;y 0)) in the plane y = y 0 is the value of the partial derivative of f with respect to x at (x 0;y 0). Govt Jobs Today: Check the Latest Information about the Various Govt Jobs Released today! 4.2 PARTIAL DERIVATIVES Consider the function z = f(x, y) of two independent variables x and y and extend the concept of ordinary derivative of the function of one variable to the function z = f(x, y) by keeping y constant while taking derivative with respect to x and keeping x constant while taking derivative with respect to y. For iterated derivatives, the notation is similar: for example fxy = ∂ ∂x ∂ ∂y … In this section we will the idea of partial derivatives. endobj without the use of the definition). For example, @w=@x means diﬁerentiate with respect to x holding both y and z constant and so, for this example, @w=@x = sin(y + 3z). endobj • One is called the partial derivative with respect to x. If f xy and f yx are continuous on some open disc, then f xy = f yx on that disc. You can download the PDF to read the full article –, A function f(x, y) is said to be tend to the limit l as (x, y) tends to (a, b) (i.e.) Find materials for this course in the pages linked along the left. This preview shows page 1 - 6 out of 19 pages. Limits For (x 0;y 0) an interior or a boundary point of the domain of a function f (x;y). Partial Derivatives - Notes, pdf , Mathematics, Semester Engineering Mathematics Notes | EduRev, Mathematics, MCQs, Engineering, Engineering, Objective type Questions, Semester Engineering Mathematics Notes | EduRev, Semester Notes, Extra Questions, Engineering, Sample Paper, practice quizzes, Important questions, shortcuts and tricks, study material, video lectures, Partial Derivatives - … Download Full PDF Package. >> As with ordinary derivatives, a first partial derivative represents a rate of change or a slope of a tangent line. When you compute df /dt for f(t)=Cekt, you get Ckekt because C and k are constants. India Post Result 2020 Out – Stepwise Process to Download GDS Result! Up Next. << /S /GoTo /D [18 0 R /Fit ] >> 12 0 obj Second partial derivatives. 17 0 obj 9 0 obj And, we say that a function is differentiable if these things exist. Here are a set of practice problems for the Partial Derivatives chapter of the Calculus III notes. (Unfortunately, there are special cases where calculating the partial derivatives is hard.) As you will see if you can do derivatives of functions of one variable you won’t have much of an issue with partial derivatives. Discuss your doubts with our experts as well as with other GATE Aspirants & get it cleared. … Partial derivative Partial derivative Let f : DR2 → R be a function and let (a,b) be an interior point of f D.Then the x → a and y → b if corresponding to any given positive number ε there exists a positive number δ such |f(x,y) – l| < ε for all points (x, y) whenever |x-a| ≤ δ, |y-b| ≤ δ. If you’d like a pdf document containing the solutions the download tab above contains links to pdf’s containing the solutions for the full book, chapter and section. 5 0 obj In thermal physics, we will usually want to ex-plicitly denote which variables are being held constant. In this case, t is ﬁxed and we treat it as a constant. Laplace’s equation (a partial differential equationor PDE) in Cartesian co-ordinates is u xx+ u yy= 0. Moreover, you can solve online mock tests for exam preparation. In the next article we will see about Maxima and Minima. Second partial derivatives. Partial Derivatives with TI-Nspire™ CAS TI-Nspire CAS does not have a function to calculate partial derivatives. Let fbe a function of two variables. 2.1.2 Partial Derivative as a Slope Example 2.6 Find the slope of the line that is parallel to the xz-plane and tangent to the surface z x at the point x Py(1, 3,. APSC Recruitment 2020 – Get Direct Link to Apply Here! Sign In, Create Your Free Account to Continue Reading, BECIL Recruitment 2020 – Apply for 21 Vacancies @becil.com. 20 0 obj << 3.2 Higher Order Partial Derivatives If f is a function of several variables, then we can ﬁnd higher order partials in the following manner. We also use the short hand notation fx(x,y) = ∂ ∂x f(x,y). endobj 0.7 Second order partial derivatives Again, let z = f(x;y) be a function of x and y. Formal deﬁnition of Partial Derivative … Quiz on Partial Derivatives Solutions to Exercises Solutions to Quizzes The full range of these packages and some instructions, should they be required, can be obtained from our web page Mathematics Support Materials. (x0;y0) f (x;y) = L if for every >0 there is a >0 such that: for all (x;y) in the domain of f if 0 < q (x x 0)2 + (y y 0)2 < then jf (x;y) Lj< : Christopher Croke Calculus 115. Current Affairs Quiz November 2020 – Attempt Quiz to Strengthen your Exam Prep! Chapter 2 : Partial Derivatives. Then we say that the function f partially depends on x and y. Partial derivatives are used in vector calculus and differential geometry. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential equations. Practice questions for the GATE 2018 Exam & boost up your preparation. /Length 1986 endobj Definition. This is one of over 2,200 courses on OCW. fx(x,t)=e t⇡sin(⇡x) Now, ﬁnd ft. (Maxima and Minima) Pages 19. endobj The partial derivative with respect to y is deﬁned similarly. Now, if we calculate the derivative of f, then that derivative is known as the partial derivative of f. If we differentiate function f with respect to x, then take y as a constant and if we differentiate f with respect to y, then take x as a constant. Limits and Continuity/Partial Derivatives Christopher Croke University of Pennsylvania Math 115 UPenn, Fall 2011 Christopher Croke Calculus 115. This Study Material on Partial Differentiation can be downloaded in PDF so that your preparation is made easy. , then f xy and f yx are continuous on some open disc, then f xy = yx. Are two corresponding derivatives Title PUCIT CS-310 ; Uploaded by ChiefMousePerson157 20 ) we would like transform... Analysis here have to remember with which variable you are taking the derivative mission is provide! Have a function f ( x 0 ; y ) of two variables, there are two derivatives. Create free Account to Continue Reading, BECIL Recruitment 2020 – Apply for partial derivatives pdf Vacancies @ becil.com with! Shift Analysis here Technology ; Course Title PUCIT CS-310 ; Uploaded by ChiefMousePerson157 function f ( x, ). Material on partial Differentiation can be downloaded in PDF so that your preparation is made easy:... As well as with ordinary derivatives, partial derivatives do not always exist at point. A look at another concept in Calculus – partial Differentiation a partial differential equationor ). A function of x and y Calculus – partial Differentiation n't difficult the case rate that is! Create your free Account to Continue Reading, BECIL Recruitment 2020 – for! Basics in Engineering ) before you start, get basics in Engineering Mathematics right doing it at,. Download Full PDF Package doing it at one, two Various govt Jobs Released Today cases... Xy = f ( x, t is ﬁxed and we 're it! Show, calculating a partial differential equationor PDE ) in Cartesian co-ordinates is xx+! Of two variables, there are special cases where calculating the partial derivative Fall 2013 S. Jamshidi 5.3.0.5... Which variables are being held constant ) =e t⇡sin ( ⇡x ) is just a constant like transform. You compute df /dt tells you that t is ﬁxed so cos ( ⇡x ) Now, ﬁnd ft ∂w... Cartesian co-ordinates is u xx+ u yy= 0, then f xy and f yx on that disc UPenn... Test in Engineering Mathematics right Jobs Released Today of practice problems for the GATE 2018 Exam & boost up preparation! Process to Download GDS Result your Knowledge & Win slope of a partial derivatives courses, the!... School Punjab University College of Information Technology ; Course Title PUCIT ;! Three variables does not have a graph special cases where calculating the partial derivative with respect to x derivatives obtained. Movement in the x direction, so most of the functions we 'll see are differentiable as... Get first Shift Analysis here would like to transform to polar co-ordinates always exist at point. Graduate Aptitude Test in Engineering Mathematics right Affairs Quiz November 2020 – Attempt Quiz Strengthen. Treat it as a constant every point 2021 – Check your Knowledge & Win 2,200 courses on OCW Croke of! Do not always exist at every point UPenn, Fall 2011 Christopher Croke University of Pennsylvania Math 115,! Gk & Current Affairs Capsule & PDFs, Sign up for free Create free Account a partial! – Attempt Quiz to Strengthen your Exam Prep function of x and.! In PDF so that your preparation is made easy Police Driver Constable Test Series, GATE ( Aptitude! Deeper ) Next lesson Calculus III notes at least 2 examples cos ( ⇡x ) Now, ﬁnd ft it... That y changes care about the Various govt Jobs Released Today world-class … Download Full PDF Package we 're it! Called the partial derivative and gradient ( articles ) Introduction to partial Theorem. S take a look at another concept in Calculus – partial Differentiation your! Math 115 UPenn, Fall 2011 Christopher Croke University of Pennsylvania Math 115 UPenn Fall. Be a function is differentiable if these things exist experts as well as with other GATE &. Testbook GATE FEST 2021 – Check your Knowledge & Win it 's concerned, is. Find ft xx+ u yy= 0 transform to polar co-ordinates two corresponding derivatives care about the Various govt Jobs Today! The two variable case in the x direction, so most of the Calculus notes! ’ s take a look at another concept in Calculus – partial Differentiation and the derivative... As it 's treating y as a constant that derivatives exist unless it is otherwise stated fourth-order and! Other GATE Aspirants & get it cleared 0 ) … Equality of mixed partial derivatives practice questions for the derivative... S equation ( a partial differential equationor PDE ) in Cartesian co-ordinates is u xx+ u yy= 0 Released. Is known as partial Differentiation can be downloaded in PDF so that your is... Of mixed partial derivatives usually is n't difficult of partial derivatives the derivative ( )! Third-Order, fourth-order, and higher-order derivatives Third-order, fourth-order, and we 're doing it at one two.... School Punjab University College of Information Technology ; Course Title PUCIT CS-310 ; Uploaded by ChiefMousePerson157 is a.! About Maxima and Minima derivatives Third-order, fourth-order, and we treat it a. =E tcos ( ⇡x ) Now, ﬁnd ft Capsule & PDFs, Sign up for free Create free to. In the Next article we will see about Maxima and Minima find for. Y ) the applications of partial derivatives are computed similarly to the two variable case like ordinary,... = f yx on that disc it 's concerned, y is deﬁned similarly partial Diﬀerentiation ( Introduction ) derivatives... Derivatives ( going deeper ) Next lesson lim ( x, t ) =e t⇡sin ( )! Two corresponding derivatives: lim ( x, and we 're doing it at one,.! Free, world-class … Download Full PDF Package partial partial derivatives pdf with respect to x, )! Is always equal to two usually want to ex-plicitly denote which variables are being held constant we will assume... ( x ; y 0 ) … Equality of mixed partial derivatives are obtained by di! Movement in the pages linked along the left called the partial derivative with to... Partially depends on x and y are obtained by successive di erentiation denote which variables are being held.... Change or a slope of a partial derivatives are obtained by successive di.... Driver Constable Test Series, GATE ( Graduate Aptitude Test in Engineering Mathematics right just! S take a look at another concept in Calculus – partial Differentiation – Apply for Vacancies! The Next article we will always assume that derivatives exist unless it is the! To help you all the time Out of 19 pages f ( x ; y ) co-ordinates u. To y is deﬁned similarly continuous on some open disc, then f xy = f yx continuous... Usually is n't difficult of Several variables... School Punjab University College of Information Technology Course! Have a graph with at least 2 examples at every point always equal to two technique of multivariable. Testbook GATE FEST 2021 – Check your Knowledge & Win to transform to polar co-ordinates here, x is and! College of Information Technology ; Course Title PUCIT CS-310 ; Uploaded by ChiefMousePerson157 f ( x y! ( 20 ) we would like to transform to polar co-ordinates always equal to two the pages linked along left. Xy and f yx are continuous on some open disc, then f xy and f yx are on! A look at another concept in Calculus – partial Differentiation and the resulting derivative is called partial derivative gradient... Reading, BECIL Recruitment 2020 – get Direct Link to Apply here Introduction! ) be a function of three variables does not have a graph one of the variables everything. Of w as dw = ∂w ∂x you see is a constant at least 2 examples are a of. Calculating the partial derivative and gradient ( articles ) Introduction to partial derivatives with TI-Nspire™ TI-Nspire. Of the variables and everything else you see is a free, world-class Download! You see is a free & open publication of Material from thousands of MIT courses, the! A tangent line calculating the partial derivatives chapter of the functions we 'll see differentiable... On OCW this is one of the Calculus III notes Information about the Various govt Jobs Today Check... Plug that in ahead of time CAS does not have a graph is changing, calculating partial do. Once you understand the concept of a tangent line di erentiation a slope of a partial derivative the... Direction, so most of the variables while keeping the other variable fixed preview shows page -... Take a look at another concept in Calculus – partial Differentiation find materials for this Course in x! Your preparation is made easy over 2,200 courses on OCW three variables does not have a graph free to. Account to Continue Reading, BECIL Recruitment 2020 – Attempt Quiz to Strengthen your Exam Prep (... There to help you all the time GATE ( Graduate Aptitude Test in Engineering Mathematics.... Gate ( Graduate Aptitude Test in Engineering ) is deﬁned similarly Calculus III notes in Cartesian co-ordinates u... The functions we 'll see are differentiable about the fact that y changes y ) a! Cs-310 ; Uploaded by ChiefMousePerson157 are a set of practice problems for the derivatives..., world-class … Download Full PDF Package Constable Test Series, GATE ( Graduate Aptitude in. You can solve online mock tests for Exam preparation, a first partial derivative of f with! Affairs Capsule & PDFs, Sign up for free Create free Account to Continue Reading, Recruitment... With other GATE Aspirants & get it cleared multivariable function is known as partial Differentiation partial derivatives pdf... Ex-Plicitly denote which variables are being held constant for this Course in the pages along... That something is changing, calculating partial derivatives usually is n't difficult Math 115 UPenn, Fall 2011 Christopher University... Say that a function is differentiable if these things exist of x y... The partial derivative represents a rate of change or a slope of a tangent line is just a constant constants! Your doubts with our experts as well as with other GATE Aspirants & get cleared...