(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose you have three functions, [itex]f_{1}(x_1),f_{2}(x_2),f_{3}(x_3)[/itex]. Consider the following expression: [itex]H=\int_{0}^{f_{1}(v_1)} G(f_2(\xi))G(f_3(\xi))d\xi[/itex], where [itex] G [/itex] is some continuous function. What is [itex] \frac{\partial H}{\partial x_{j}}[/itex], [itex]j\neq 1[/itex]?

3. The attempt at a solution

According to me, all this derivatives are zero. However, I am not quite sure of this because, by applying the chain rule I obtain: [itex] \frac{\partial H}{\partial x_{2}}=\frac{\partial H}{\partial f_{2}}\frac{\partial f_2}{\partial x_{2}}[/itex]. Since [itex]\frac{\partial H}{\partial f_{2}}[/itex] and [itex]\frac{\partial f_2}{\partial x_{2}}[/itex] are both nonzero (known data), then the whole thing should be different from zero. Am I wrong here?

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# What is the derivate of this expression?

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