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 $\displaystyle \sqrt{x} = x^{1/2}$? Do you know how to differentiate $\displaystyle \sin x$? Do you know how to simplify the resulting expression for the derivative?
Show your working and state where you get stuck.
$\displaystyle \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.