Question

Find the derivative of cos^2(3sqrt(x))

For my answer I get (6cos*3sqrt(x))/2sqrt(x)


But the book says the answer is (-3/sqrt(x))*cos(3sqrtx)*sin(3sqrtx)

Answer 1

\[ \frac{d}{dx} u^2 = 2 u \frac{d}{dx}u \]
if u is cos(stuff)
\[ \frac{d}{dx} \cos(stuff)^2 = 2 \cos(stuff) \frac{d}{dx}\cos(stuff) \]

we know the derivative of cos is sin (the rule is):
\[ \frac{d}{dx} \cos(u) = \sin(u) \frac{d}{dx}u \]
so you definitely should get a sin in your answer.