Question

What is the second derivative of `f(x)=cos(-x)`?

Answer 1

`-cos(-x)`

Explanation:

You can compute this in two ways: either you observe that `cos(-x)=cos(x)`, and so you have

`f(x)=cos(x)`
`f'(x)=-sin(x)`
`f''(x)=-cos(x)`

Or you use the chain rule and compute

`f(x)=cos(-x)`
`f'(x)=-sin(-x) * d/dx (-x) = -sin(-x) * -1 = sin(-x)`
`f''(x)=cos(-x) * d/dx (-x) = cos(-x) * (-1) = -cos(-x)`