# Math Help - Trig Function Derivs.

1. ## Trig Function Derivs.

Find the derivative of the function below. Remember to use pi for π.
g(x) = sin^2(10x) - pix

alright just need to know how to do this problem.
thanks

mathlete

2. Originally Posted by mathlete
Find the derivative of the function below. Remember to use pi for π.
g(x) = sin^2(10x) - pix

alright just need to know how to do this problem.
thanks

mathlete
$g(x)=sin^2(10x) - \pi x$

$g(x) = h(x) - \pi x$

To find the derivative, apply power rules, then chain and trig rules...

$g'(x) = h'(x) - \pi$

I am using the h function to show the chain rule.

Chain rule says:

$h(x) = f(R(x))$
$h'(x)=f'(R(x))*R'(x)$

We have:

$h(x) = sin^2(10x)$
$h'(x) = 2sin(10x)*cos(10x)*10$

It's a double chain... now plug that back in!

3. Well, we know a few things:

$\frac{dy}{dx}[sin(x)] = cos(x)$

$\frac{dy}{dx}[sin(10x)] = 10cos(10x)$

$sin^2(10x) = sin(10x)sin(10x)$

$g(x) = \underbrace{sin(10x)sin(10x)}_{\text{Use Product Rule}} - \underbrace{\pi x}_{\text{Use Power Rule}}$

Use the product rule for $sin^2(10x)$ and using the above information, you should arrive at the derivative.