This problem is tricky because instead of having x all by itself as the upper limit of integration, we have x2:
If the problem were asking for just the derivative of F(x), we would be all set, because we know
F'(x) = sin(x2).
Instead, the problem is asking for the derivative of
which happens to be the same thing as F(x2). We can find the derivative of F(x2) using the chain rule. We have F as the outside function and x2 as the inside function. So
F'(x) = sin(x2),
F'(x2) = sin((x2)2) = sin(x4).
Putting this back into the earlier equation,