I am REALLY not very good at this because I was away when they were teacher it at school and so I really need to brush up on this but anyway here are a few questions and could someone please help out I'd really appreciate it

**Differentiate:** **a) x^2 sin (-x) **

Note that we can rewrite $\displaystyle \sin(-x)$ as $\displaystyle -\sin(x)$ due to the fact that sine is an odd function. Then apply product rule to $\displaystyle -x^2\sin(x)$. Now that you know these derivatives better, it should be a breeze!

b) sin^2 x

Apply the chain rule. The way that Matt Westwood computed the derivative is great

c) cosx.tan 3x

Apply the product rule. Note that the chain rule is required when we end up differentiating $\displaystyle \tan({\color{red}3x})$

d) x/tan x

The way that Matt Westwood computed the derivative is perfectly fine. However, you can rewrite the equation as $\displaystyle x\cot(x)$. You can use product rule here. Note that his answer and the answer you will get will be the same, but in alternative forms.

e) x^3 - 2 sin (x/3)

This should be a breeze for you now, but keep in mind that you will need to apply the chain rule when you differentiate $\displaystyle 2\sin\left(\frac{x}{3}\right)$.

I'm sorry there are many questions here but I really don't know how to do these that well and I was away when they taught it at school