Calculus › Section C · Derivatives › Topic C.5

Implicit differentiation

Many curves refuse to be written as y in terms of x: circles, ellipses, the orbits of physics. Implicit differentiation finds their slopes anyway, without ever solving for y.

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In this topic

Curves that are not functions
The key move: y is a function of x
Worked example: an ellipse
The four-step routine
Worked example: a curve with a product term
Worked example: a tangent line
Level and vertical tangents from the formula
Second derivatives, implicitly
Where this shows up
Common mistakes to avoid
Key takeaways

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Standards: 3

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