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

Oct 26, 2016

You could start off by saying that:

y=k(x)

If this is the case:

$y = - 3 \cos x$

$- \frac{1}{3} \cdot y = \cos x$

Now from here you can use implicit differentiation to get $\frac{\mathrm{dy}}{\mathrm{dx}}$.

$- \frac{1}{3} \cdot \frac{\mathrm{dy}}{\mathrm{dx}} = - \sin x$

Which means that:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 \sin x$

And this means that:

$k ' \left(x\right) = 3 \sin x$

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

If $f \left(x\right) = \cos x$, $f ' \left(x\right) = - \sin x$.

This is very important.