Question

Differentiate

\[xsin^2x\]

Answer 1

product rule:
[x*sin^2x]' = [x]'*sin^2x + x*[sin^2x]'
=1*sin^2x + x*(2*sinx*cosx)
= sin^2x + 2xsinxcosx
or using double angle formula
= sin^2x + xsin(2x)

Answer 2

How do you differentiate sin^2x. That's what I had trouble with.

Answer 3

but a faster way would be the chain rule...