# Math Help - Finding a Derivative from an Integral

1. ## Finding a Derivative from an Integral

Third question of the day...

p(x)=INTGRL(a=1, b=SQRROOTx) sin^5T. find DY/DY

Normally, I know how to do this problem, but I don't know when a is 1. I've only done them when a is equal to zero

2. Originally Posted by Super Mallow
Third question of the day...

p(x)=INTGRL(a=1, b=SQRROOTx) sin^5T. find DY/DY

Normally, I know how to do this problem, but I don't know when a is 1. I've only done them when a is equal to zero
Do you mean
$p(x) = \int_1^{\sqrt{x}}~sin^5(t)~dt$

and to find $\frac{dp}{dx}$?

-Dan

3. Yes, that's exactly it

4. Originally Posted by Super Mallow
Yes, that's exactly it
Use the second fundamental theorem with the chain rule:

$\frac d{dx} \int_a^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)$