# Homework Help: Find derivative using FTC1

1. Nov 25, 2008

### aeonsky

I need to find the derivative of the function below...

1. The problem statement, all variables and given/known data

$G(x) = \int_{x}^{1} cos(\sqrt{t}) dt$

2. Relevant equations

FTC1

If f is continuous on [a,b], then the function g defined by

$g(x) = \int_{a}^{x} f(t) dt$ $a \leq x \leq b$

is continuous on [a,b] and differentiable on (a,b) and $g'(x) = f(x)$

3. The attempt at a solution

Would it be $-cos(sqrt(t))$

Thanks for the time!

Last edited: Nov 25, 2008
2. Nov 25, 2008

### HallsofIvy

It would be $-cos(\sqrt{x})$, not t.

3. Nov 25, 2008

### lurflurf

First you might reverse the limits, which reveses the sighn. FTC1 says the derivative of the integral of a function is the function. Differendiation cancels integration.