HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Harder 2-Unit

Implicit differentiationEdit

Implicit differentiation is a method of differentiating an expression in   and  , where   and   are related in some manner and neither are constant.

For example, one could differentiate   with respect to   as follows:

Using the chain rule:
 

It is useful to think of implicit differentiation as normal differentiation with respect to  , only whenever you come across a term with  , you multiply the differentiated term by  .

Another example: find the derivative   of  

Working: