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GeezerVison is showing mathworld.wolfram.com — Implicit Differentiation -- from Wolfram MathWorld 
Implicit Differentiation
Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable For example, the implicit equation
can be solved for
and differentiated directly to yield
Differentiating implicitly instead gives
Plugging in
Implicit differentiation is especially useful when See alsoDerivative, Differentiation Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
More things to try: ReferencesAnton, H. "Implicit Differentiation." §3.6 in Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.Referenced on Wolfram|AlphaImplicit DifferentiationCite this as:Weisstein, Eric W. "Implicit Differentiation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ImplicitDifferentiation.html Subject classifications | ||||||||||||||
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while treating the other variables as unspecified functions
of 
.
![d/(dx)[xy]=d/(dx)[1]](/api/image?u=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FImplicitDifferentiation%2FInline3.svg){kind=small}
verifies that this approach gives the same result as before.
is needed, but it is difficult or inconvenient to solve
for 
in terms of 
.