1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Partial derivative concept

  1. Apr 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Given the partial derivative df/dx= 3-3(x^2)

    what is d^2f/dydx?

    I'm not sure if the answer would be 0, since x is held constant, or if it would remain 3-3(x^2) (since df/dx is a function of x now?)
  2. jcsd
  3. Apr 27, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    The answer is one of those choices. Here, think about it like this:

    You are given a function:


    You want to find: [tex]\frac{\partial g}{\partial y}[/tex]

    What is that derivative? Now, what if: [tex]g(x)=\frac{\partial f}{\partial x}[/tex]

    Does this change the partial derivative of g with respect to y?
  4. Apr 27, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    You were right the first time. With x held constant the d/dy is just differentiating a constant. It's 0.
  5. Apr 27, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    As is always true, with "nice" functions, the two mixed derivatives are equal. You could find [itex]\partial^2 f/\partial x\partial y[/itex] by differentiating first with respect to x, then with respect to y: first getting -6x and then, since it does not depend on y, 0. Or you could differentiate first with respect to y, then with respect to x: getting 0 immediately and then, of course, the derivative of "0" with respect o x is 0.

    I, and I suspect many who read your post, was momentarily taken aback since I thought you were "holding x constant" through both derivatives. But you are correct: since this function does not depend on y, any derivative of it with respect to y, is 0.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Partial derivative concept
  1. Partial derivative (Replies: 1)

  2. Partial derivative (Replies: 2)

  3. Partial derivatives (Replies: 1)

  4. Partial derivative (Replies: 21)

  5. The partial derivative (Replies: 2)