Derivative of a integral function?

  • Thread starter pellman
  • Start date
  • #1
675
4
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]

and

[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?
 

Answers and Replies

  • #2
[tex]
\frac{d}{dx}\int^x_y f(x,u)du = \int^x_y \frac{d}{dx}f(x,u)du+f(x,x).
[/tex]
 
  • #3
675
4
Thanks, Pere.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
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.
 

Related Threads on Derivative of a integral function?

  • Last Post
Replies
3
Views
5K
Replies
4
Views
694
Replies
4
Views
1K
Replies
6
Views
712
Top