# How do you differentiate cos^2(3x)?

Dec 10, 2016

Use the Chain Rule!

If we think of ${\cos}^{2} \left(x\right)$ as our outside function, and $3 x$ as our inside function:

We would calculate as follows:

$\frac{d}{\mathrm{dx}} {\cos}^{2} \left(x\right) \cdot \frac{d}{\mathrm{dx}} \left(3 x\right)$

Thus we would get:

$- 2 \sin \left(3 x\right) \cos \left(3 x\right) \cdot 3$

$= - 6 \sin \left(3 x\right) \cos \left(3 x\right)$