Topics › Calculus › Implicit Differentiation — Differentiate Implicitly Defined Relations
Calculus · DER

Implicit Differentiation — Differentiate Implicitly Defined Relations

Differentiate both sides with respect to x; treat y as a function of x so d/dx[y^n] = n·y^(n−1)·(dy/dx). Solve for dy/dx.

CalculusCommon Core FUN-3.DDERVerified correct ✓

Worked examples

Given x² + y² = 9, use implicit differentiation to find dy/dx. Then evaluate dy/dx at (2, 2.24). Round to 4 decimal places.
Answer: -0.8929
Given x² + y² = 9, use implicit differentiation to find dy/dx. Then evaluate dy/dx at (2, 2.24). Round to 4 decimal places.
Answer: -0.8929

Every problem on Pounce is generated and checked by code — never a wrong answer key.

Master Implicit Differentiation — Differentiate Implicitly Defined Relations

Code-verified problems at exactly the right level, explained the way your kid learns.

Start your free trial 🐾

Build up to this

Chain Rule — Differentiate Composite FunctionsProduct Rule — Differentiate a Product of Two Functions

More Calculus topics

Evaluate Limits Algebraically — Substitution and FactoringEvaluate Trigonometric Limits — sin(x)/x as x→0Limits at Infinity — End Behavior of Rational FunctionsTest Continuity at a Point — Three-Part DefinitionDerivative from the Limit DefinitionPower Rule — Differentiate Polynomial FunctionsProduct Rule — Differentiate a Product of Two FunctionsChain Rule — Differentiate Composite Functions