# Integral Derivative

1. Oct 9, 2006

### sapiental

g(x) = integral 0 to lnx (sin(t)+t^3/2))dt

find d/dx g(x):

let u = lnx

= sin(u) + u^3/2 du/dx
= sin(lnx)(1/x) + x^3/2(1/x)

Thanks

Last edited: Oct 9, 2006
2. Oct 9, 2006

### HallsofIvy

What is your question?

3. Oct 9, 2006

### drpizza

I believe what you need to examine is the fundamental theorem of calculus, part 2. Check your text.

edit: in that section, you'll probably see some examples where they find the derivative of the integral of some function...

Last edited: Oct 9, 2006