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