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.
could some one show me in steps how to go about this one.
thanks
mathlete
$\displaystyle g(x)=sin^2(10x) - \pi x$
$\displaystyle g(x) = h(x) - \pi x$
To find the derivative, apply power rules, then chain and trig rules...
$\displaystyle g'(x) = h'(x) - \pi$
I am using the h function to show the chain rule.
Chain rule says:
$\displaystyle h(x) = f(R(x))$
$\displaystyle h'(x)=f'(R(x))*R'(x)$
We have:
$\displaystyle h(x) = sin^2(10x)$
$\displaystyle h'(x) = 2sin(10x)*cos(10x)*10$
It's a double chain... now plug that back in!
Well, we know a few things:
$\displaystyle \frac{dy}{dx}[sin(x)] = cos(x)$
$\displaystyle \frac{dy}{dx}[sin(10x)] = 10cos(10x)$
$\displaystyle sin^2(10x) = sin(10x)sin(10x)$
$\displaystyle g(x) = \underbrace{sin(10x)sin(10x)}_{\text{Use Product Rule}} - \underbrace{\pi x}_{\text{Use Power Rule}}$
Use the product rule for $\displaystyle sin^2(10x)$ and using the above information, you should arrive at the derivative.