TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Implicit Differentiation
If 
, how would you differentiate this with respect to x? There are three ways:
Way One
Rewrite it as 
and differentiate as normal.
Way Two
Since 
Way Three
Differentiate term by term and use the chain rule:
The right hand side of this equation is 1, since the derivative of x is 1. However, to work out the left hand side we must use the chain rule.
The left hand side becomes:
(although it is not correct to do so, at this level you can think of dy/dx as a fraction in the chain rule. In the line above, imagine that you can cancel the 'dy' s, leaving d/dx and y³, which is what we had in the previous line).
Therefore,
So
In this example, method (2) is clearly the easiest. However, there are cases when the only possible method is (3).
Example
Differentiate 
, with respect to x.
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