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