find f'(x). Please explain?

Question

If f(x)=sqrt{x}sin{x}, find f'(x).

Answer 1

The function f(x) = √x sinx

Differentiating on each side with respect to x .

Apply product rule in derivatives.

d/dx (uv) = uv'+ vu'

u = √x, v = sinx

u' = 1/2√x , v' = cosx

f'(x) = √x cosx + sinx(1/2√x)

= √x cosx + (sinx)/2√x

f'(x) = (2x cosx + sinx)/2√x.