Derivative of a definite integral $\frac{\partial}{\partial x(i)}\int_{i=0}^{A}[x(i)]^{\alpha}di$

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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.