Question

How do you find the derivative of `f(x) = 2x(sinx)cos(x)`?

Answer 1

The answer is `=sin2x+2xcos2x`

Explanation:

Use `2sinxcosx=sin2x`
`:. f(x)=xsin2x`
We use the product rule to find the derivative
`(uv)'=u'v+uv'`
`u=x` `=>` `u'=1`
`v=sin2x` `=>` `v'=2cos2x`
so, `f'(x)=sin2x+2xcos2x`