# Thread: Calculus - Product Rule

1. ## Calculus - Product Rule

I'm stuck on this problem

square root of x times sin(x)

How do you differentiate this function using the product rule?

2. Originally Posted by PMoNEY23
I'm stuck on this problem

square root of x times sin(x)

How do you differentiate this function using the product rule?
Do you know the formula for the product rule? Do you know how to differentiate $\sqrt{x} = x^{1/2}$? Do you know how to differentiate $\sin x$? Do you know how to simplify the resulting expression for the derivative?

Show your working and state where you get stuck.

3. yes i know the formula and this is where im stuck at:

edited:
(x^1/2)[cos(x)]+[1/2x^1/2](sin(x))

4. Originally Posted by PMoNEY23
yes i know the formula and this is where im stuck at:

edited:
(x^1/2)[cos(x)]+[1/2x^1/2](sin(x))
$\sqrt{x} \cos x + \frac{\sin x}{2 \sqrt{x}} = \frac{2x \cos x}{2 \sqrt{x}} + \frac{\sin x}{2 \sqrt{x}} = \frac{2x \cos x + \sin x}{2 \sqrt{x}}$.

Note: If you show your work and state where you're stuck it can save people wasting time posting things that you already know how to do.