I am doing a maths unit at uni this year as a mature age student. I used to be good at maths, but dropped out of high school after year 8 and I'm struggling a bit with this. There is a lot of assumed knowledge and my lecturer seems to explain the concepts like she is talking to someone who already knows them.

I have handed in 3 assignments so far and got above 90% for two of them, but failed the third. I don't understand why I can catch onto some concepts easily and totally miss the point of others...

This week is on differentiation and derivatives and I don't get it at all! Anyone that might be able to explain?

The specific questions I have to answer are:

Find the derivatives of the following functions

y = 2x^4+3x-1-x^-2

y = (x + 3)^1/2

y = e^x2+4x-1 (everything after e is a power)

y = e^-x ln x

y = ln (x^2+1/x)

y = 1+cos x/1-sin x

Find the second derivative of y = e^x sin x

Find the third and fourth derivatives of the function y = 4x^6+3x^2-21-x^-3

Find the tangent to the curve y = -x^3+ 2x-1

Any help would be much appreciated. I know it says to state what you have done so far, but that is the problem, I don't understand any of it. I don't get what the derivative is, why I need to know what it is, or how to find it? I've been staring at my lecture notes all day and nothing has sunk in at all. About to give up.