Take a derivative of a definite integral $\frac{\partial}{\partial x(i)}\int_{i=0}^{A}[x(i)]^{\alpha}di$, where A is some constant.
The answer should be $\alpha[x(i)]^{\alpha - 1}$
My take (I'm not particularly good at calculus):
Rewrite $\frac{\partial}{\partial x(i)}\int_{i=0}^{A}[x(i)]^{\alpha}di$ as:
$\frac{\partial}{\partial x(i)}\int_{i=0}^{A}[x(i)]^{\alpha}dx(i)\frac{di}{dx(i)}$
Then take the derivative as follows:
$[x(i)]^{\alpha}\frac{di}{dx(i)}$
And basically I'm stuck here (told you I'm no good).
Any help would be highly appreciated.