Question

If f (x) = (4 sin x + 2)^(1/2), f' (0) = ???

Answer 1

Use u^n du rule here.

u = 4sinx + 2

f(x) = (4sinx + 2)^1/2

Chain rule

f'(x) = (1/2)(4cosx)(4sinx+2)^(-1/2)
f'(x)=2cosx(4sinx+2)^-1/2

Answer 2

To find the derivative of a square root use this fast trick! All you have to do is just find the derivative of the expression under the root!