Question

How do you find the derivative of `cos(-x)`?

Answer 1

See the explanation.

Explanation:

Before learning the chain rule, you need to use a fact from trigonometry:

`cos(-x) = cosx`

Therefore,

`d/dx(cos(-x) = d/dx(cosx) = -sinx`

(By the way `sin(-x) = -sinx`, so the answer couls be written `sin(-x)`.

Using the chain rule

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

`= -sin(-x)(-1) = sin(-x) = -sinx`