Originally Posted by

**Paymemoney** Hi

I need help on the following:

1)Differentiate with respect with x: $\displaystyle sin^2(x)$

I got $\displaystyle 2sin(x)cos(x)$, however i don't understand why the book's answer is $\displaystyle sin(2x)$.

2)Differentiate with respect with x: $\displaystyle arcos(\sqrt{1-x^2})$

This is what i have done:

$\displaystyle \frac{dy}{dx} = \frac{-0.5(1-x^2)^{-0.5} * 2x}{\sqrt{1-(\sqrt{1-x^2})^2}}$

$\displaystyle = \frac{x}{\sqrt{1-x^2}\sqrt{x^2}}$

What would i do next?

3) Prove that $\displaystyle \frac{d}{dx}(arccos(x) = \frac{-1}{\sqrt{1-x^2}}$

How would i approach this??

P.S