Dear Amberosia32,

For the first and second problems you should use the chain rule. That is if y and z are functons of x,

.

eg:

Similar method could be used to differentiate

and

For a curve in two dimention(including a independent and dependent variable.)

gives the tangent of the curve.

Therefore you could differentiate the equation, and afterwards subject

,

Subject

and you would get,

Here I have used the Leibniz's theorem in addition to the chain rule,

That is if v and u are two functions of x,

Hope these things will help you to understand differentiation. But if you have any questions please don't hesitate to reply me.