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!

Gradient Problem

  1. Jan 17, 2009 #1
    Define [tex] f: R^{2} \rightarrow R , by f(x,y) = \int^{sin(x sin(y sin z))}_{a} g(s) ds [/tex]

    where g:R -> R is continuous. Find the gradient of f.

    I tried using the FTC, and differentiating under the integral, but did not get anywhere,

    thanks for any suggestions.
  2. jcsd
  3. Jan 17, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, the FTC, together with the chain rule should work. Basically, you are saying that
    [tex]f(x,y)= \int_0^u(x,y) g(s)ds[/tex]
    where u(x,y)= x sin(x sin(y sin(x))).
    [tex]\frac{df}{du}= g(u)[/tex]
    [tex]\frac{\partial f}{\partial x}= g(u)\frac{\partial u}{\partial x}[/tex]
    [tex]\frac{\partial f}{\partial y}= g(u)\frac{\partial u}{\partial y}[/tex]

    So the question is really just: What are [itex]\partial u/\partial x[/itex] and [itex]\partial u/\partial y[/itex]f?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Gradient Problem
  1. Gradient Problem (Replies: 1)

  2. Gradient problem (Replies: 1)

  3. Gradient problem (Replies: 5)