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# 3.2 Implicit Differentiation

Jillian Holbrook

279Β resources
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## What is Implicit Differentiation?

π₯Watch: AP Calculus AB/BC - Implicit Derivatives
Back in pre-calculus, you likely learned or talked about how there are two different types of equations: explicit equations and implicit equations.
An explicit equation is written such that y is isolated on one side.Β  For example, y=2x+3 is an explicit equation. We know that for each value of x, there will only be one value of y.
Implicit equations are not as straightforward.Β  Most of the time, an implicit equation will have x and y on the same side.Β  So if x and y are on the same side, how can we differentiate an implicit equation?

## How to Differentiate Implicitly π΅

First off, letβs review the notations we can use for derivatives:
Implicit Differentiation does not use the fβ(x) notation.Β  Instead, we will use the dy/dx and y' notations.
There are three main steps to successfully differentiate an equation implicitly.
1. Get the yβs isolated on one side
2. Factor out yβ
3. Isolate yβ
Letβs look at an example to apply these steps.Β Β

## Implicit Differentiation Practice π

Youβll be a pro at implicitly differentiating in no time! Try the practice problems below and check them when youβre finished in the corresponding section at the end of this guide.

Browse Study Guides By Unit
πUnit 1 β Limits & Continuity
π€Unit 2 β Fundamentals of Differentiation
π€π½Unit 3 β Composite, Implicit, & Inverse Functions
πUnit 4 β Contextual Applications of Differentiation
β¨Unit 5 β Analytical Applications of Differentiation
π₯Unit 6 β Integration & Accumulation of Change
πUnit 7 β Differential Equations
πΆUnit 8 β Applications of Integration
π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
βΎUnit 10 β Infinite Sequences & Series (BC Only)
π§Multiple Choice Questions (MCQ)
βοΈFree Response Questions (FRQ)
πBig Reviews: Finals & Exam Prep