# Thread: Derivative of nested trigonometric functions

1. ## Derivative of nested trigonometric functions

Hello Everyone,

Today I got stuck on a group of similar problems and wanted to present an example of one.

I have have the following problem $\displaystyle Dx[sin^2(sin \pi \theta)]$

The way I solve it is the following:

Using the chain rule over and over again...

$\displaystyle 2u * \frac{d}{d _\theta} u$
$\displaystyle u = sin(sin \pi \theta)$

$\displaystyle 2[sin(sin \pi \theta)] \frac{d}{d _\theta} sin(sin \pi \theta)$

$\displaystyle 2[sin(sin \pi \theta)]$ $\displaystyle cos( sin \pi \theta) \frac{d}{d _\theta} sin(\pi \theta)$

$\displaystyle 2[sin(sin \pi \theta)]$ $\displaystyle cos( sin \pi \theta) cos(\pi \theta) \frac{d}{d _\theta} (\pi\theta)$

= $\displaystyle 2[sin(sin \pi \theta)]$ $\displaystyle cos( sin \pi \theta) cos(\pi \theta) (\pi)$

Wolframalpha tells me the answer is: $\displaystyle \pi sin(2sin\pi\theta)cos(\pi\theta)$

Did I not simplify correctly? Din't use the product rule at some point?
I'm still a bit confused of which rules to use.

2. ## Re: Derivative of nested trigonometric functions

No worries, just simplify using a trig identity