# Thread: find the derivative of an integral?

1. ## find the derivative of an integral?

how do you find the derivative of an integral?
for example $y=cosu^8du$ on [cosx,4x]. the derivative of $cosu^8=8u^7*-sinu^8$ but i don't think that's what the question is asking for.

2. Is this what you mean?:

$\frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)$

If so, go for it.

3. so would that be $4cos((4x)^8)-cos(cos^8x)(-sinx)$?