Question

How do you find `f'(0)` if `f(x)=sin^2(3-x)`?

Answer 1

The answer is: `-sin6`.

This is because, applying the chain rule:

`y'=2sin(3-x)* cos(3-x)* (-1)` and

`y'(0)=-2sin(3-0)cos(3-0)=-2sin3cos3=`

`=-sin6`.

Remembering that: `sin2alpha=2sinalphacosalpha`.