1. Limited time only! Sign up for a free 30min personal 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!

Derivative of a integral function?

  1. Jul 1, 2010 #1
    How does one work the following?

    [tex]\frac{d}{dx}\int^x_y f(x,u)du[/tex]

    I know that (given certain assumptions about the function f)

    [tex]\frac{d}{dx}\int^x_y f(w,u)du=f(w,x)[/tex]


    [tex]\frac{d}{dx}\int^c_y f(x,u)du=\int^c_y \frac{df}{dx}(x,u)du[/tex]

    but how do we put them together?
  2. jcsd
  3. Jul 1, 2010 #2
    \frac{d}{dx}\int^x_y f(x,u)du = \int^x_y \frac{d}{dx}f(x,u)du+f(x,x).
  4. Jul 2, 2010 #3
    Thanks, Pere.
  5. Jul 2, 2010 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    In general, Lagrange's formula:
    [tex]\frac{d}{dx}\int_{\alpha(x)}^{\beta(x)} f(x,t)dt= f(x,\beta(x))\frac{d\beta}{dx}- f(x, \alpha(x))\frac{d\alpha}{dx}+ \int_{\alpha(x)}^{\beta(x)} \frac{\partial f}{\partial x} dt[/tex]

    In this particular problem y is independent of both x and u and can be treated as a constant: dy/dx= 0.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Derivative of a integral function?
  1. Functional Derivative (Replies: 0)