Question

How do you find the second derivative of `sin(2x)`?

Answer 1

`f''(x)=-4sin 2x`

Explanation:

Let `f(x)=sin 2x`.

By `(sin x)'=cos x` and Chain Rule,

`f'(x)=cos 2x cdot(2x)'=2cos 2x`

By `(cos x)'=-sin x` and Chain Rule,

`f''(x)=-2sin 2x cdot (2x)'=-4sin 2x`

I hope that this was clear.