This problem is tricky because instead of having *x* all by itself as the upper limit of integration, we have *x*^{2}: Let
If the problem were asking for just the derivative of *F*(*x*), we would be all set, because we know *F* '(*x*) = sin(*x*^{2}).
Instead, the problem is asking for the derivative of which happens to be the same thing as *F*(*x*^{2}). We can find the derivative of *F*(*x*^{2}) using the chain rule. We have *F* as the outside function and *x*^{2} as the inside function. So Since *F *'(*x*) = sin(*x*^{2}),
we have *F* '(*x*^{2}) = sin((*x*^{2})^{2}) = sin(*x*^{4}).
Putting this back into the earlier equation, |