Question

What is the derivative of `(sin(x))(Cos^2(x))`?

Answer 1

Never forget that `cos^2x = (cosx)^2`.

`y = sinxcos^2x`

is a product `y = uv`
Its derivative is `y' = u'v+uv'`

To differentiate `v = cos^2x`, we'll need the chain rule.
`d/dx(cos^2x) = 2cosx d/dx(cosx) = 2cosx(-sinx) = -2sinxcosx`

`y' = d/dx(sinxcos^2x) = (cosx)(cos^2x)+(sinx)(-2sinxcosx)`

`= cos^3x - 2sin^2xcosx`.

You may rewrite this answer to taste.