Further Differentiation

Differentiating Functions of ‘y’ with Respect to ‘x’
Sometimes you want to differentiate ‘y2’ or sin y instead of a function of x
To do this, follow the golden rule: 

Differentiating Implicit Functions
Sometimes x and y are given as a jumbled equation rather than explicitly
saying x= or y=
In this case, differentiate both sides with respect to x to find the derivative
You can also apply the product rule to implicit functions

Often it is nicer (and easier) to take natural logs of both sides when
differentiating complex implicit functions

Standard Results