Question

How do you differentiate `k(x)=-3 cos x`?

Answer 1

You could start off by saying that:

y=k(x)

If this is the case:

`y=-3cosx`

`-1/3*y=cosx`

Now from here you can use implicit differentiation to get `(dy)/(dx)`.

`-1/3*(dy)/(dx)=-sinx`

Which means that:

`(dy)/(dx)=3sinx`

And this means that:

`k'(x)=3sinx`

Realistically speaking, if you are studying differentiation, you've got to memorise:

If `f(x)=cosx`, `f'(x)=-sinx`.

This is very important.