# Homework Help: What is the derivate of this expression?

1. Jan 20, 2012

### cris(c)

1. The problem statement, all variables and given/known data
Suppose you have three functions, $f_{1}(x_1),f_{2}(x_2),f_{3}(x_3)$. Consider the following expression: $H=\int_{0}^{f_{1}(v_1)} G(f_2(\xi))G(f_3(\xi))d\xi$, where $G$ is some continuous function. What is $\frac{\partial H}{\partial x_{j}}$, $j\neq 1$?

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: $\frac{\partial H}{\partial x_{2}}=\frac{\partial H}{\partial f_{2}}\frac{\partial f_2}{\partial x_{2}}$. Since $\frac{\partial H}{\partial f_{2}}$ and $\frac{\partial f_2}{\partial x_{2}}$ are both nonzero (known data), then the whole thing should be different from zero. Am I wrong here?