Implicit Differentiation

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Oct 27, 2024
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- Derivatives The Easy Way
- The Chain Rule

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Implicit and Explicit Functions

An explicit function is an function expressed as y = f(x) such as

$y = \text{sin}\; x \nonumber$

y is defined implicitly if both x and y occur on the same side of the equation such as

$x^2 + y^2 = 4 \nonumber$

we can think of y as function of x and write:

$x^2 + y(x)^2 = 4 \nonumber$