Differentiate an integration of a function with respect to that function itself

[helenwang413]

Hi,

I am stuck in a differentiation problem. I need to find the derivative of an integration of an unknown function with respect to the function itself, and then set the derivative to zero in order to find the form of the funtion which gives the minimum of its integration. For example, find a function w(r) which minimize its integration over range [0, R], you set the derivative of the integration w.r.t w(r) to zero.

I hope I've managed to describe the problem clearly. Any help would be greatly appreciated!

Thanks a lot!

Helen

 

[HallsofIvy]

I am tempted to say that
[tex]\frac{d}{df}\int f(x)dx[/itex] is, by the chain rule, <br /> $$\frac{f(x)}{\frac{df}{dx}}$$<br /> <br /> But your problems sounds like a "calculus of variations" problem. What do you know about that?[/tex]