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