Hello!
I have a quick question about a question I'm not too sure about...
y = 2sin^2(x)
What's the derivative?
I'm thinking 4sin(x), am I right?
Well you have a chain rule question. So just use the chain rule, don't guess your answers.
Firstly, the chain rule $\displaystyle \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} $
we have $\displaystyle y = 2 \sin^2 x$
so let $\displaystyle u = \sin x$
$\displaystyle \frac{du}{dx} = \cos x $
$\displaystyle y = 2u^2$
$\displaystyle \frac{dy}{du} = 4u$
$\displaystyle \Rightarrow \frac{dy}{du} = 4 \sin x$
then $\displaystyle \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} $
$\displaystyle \Rightarrow \frac{dy}{dx} = 4 \sin x \cdot \cos x$
and your done.