Find the derivative of cos(sqrtx)^3

Question

I am not sure how to do this. So far I did Cos(x^(1/2)^3

So I did the chain rule to make Cos(u) where u = x^(3/2)

Then I got -Sin(sqrtx)^3*(3/2)x^(1/2)

Which then simplifies to (-3Sin(sqrtx)(sqrx))/2

What did I do wrong?

Answer 1

Assuming the correct function is

 

f(x) = cos[(√x)³] = cos(x^3/2),

 

use the chain rule and get

 

f'(x) = -sin(x^3/2) * (3/2)x^1/2 = (-3/2) [sin(x^3/2)] x^1/2