Tangent Line & Differentiating Trig Identities ~ Help Needed

**So I'm going through my Mid Term review and I continue to come across the same problems I've been dealing with on past tests and such.**

It's going to be a multiple choice test, but when I come to tangent lines on a MC test I just plug things in and test them with the calculator...That's not a good idea so I'm wondering what exactly is the method for getting the tangent line?

The problem I have is f(x) = x(1-2x)^3 , find the tangent line at point (1, -1) and the answer is y = -7x+6

I don't understand how to get that answer.

~~ And another general question:

When you are taking the derivitive of trigonometric values, are there separate rules for them compared to before? Like, what would the derivitive of y = tan(x) - cot(x) be?

Thanks BUT more depth about trig

differentiated: tanx = sec(x)^2

cotx = -csc(x)^2

sinx = cosx

-cosx = sinx

**Can anyone complete this chart? with positive and negative for the values?**

Everything in that post helped, but when differentiating, I'm not quite sure what to think of trig identities. Up there is all I know at this point x.X