Question

Find f '(x) for f(x)= sqrt(sin (4x))?

Answer 1

Can you find the derivative of sqrt(x) ?

Answer 2

Re-writing the square root as a 1/2 exponent may help. And you need to be familiar with the chain rule.

Answer 3

f'(x) = 4Cos4x/2sqrt(sin4x) using the formula f'(x) = dx/2sqrt(x)

or take the long route.


f'(x) = 0.5 (sin4x)^(-0.5) * 4(cos4x)

= 4cos4x/2sqrt(sin4x)