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# Implicit Differentiation

Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable while treating the other variables as unspecified functions of .

For example, the implicit equation

 (1)

can be solved for

 (2)

and differentiated directly to yield

 (3)

 (4) (5) (6) (7)

Plugging in verifies that this approach gives the same result as before.

Implicit differentiation is especially useful when is needed, but it is difficult or inconvenient to solve for in terms of .

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## References

Anton, H. "Implicit Differentiation." §3.6 in Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.

## Referenced on Wolfram|Alpha

Implicit Differentiation

## Cite this as:

Weisstein, Eric W. "Implicit Differentiation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ImplicitDifferentiation.html