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?