Topics › Calculus › Related Rates — Implicit Differentiation with Respect to Time
Calculus · DER

Related Rates — Implicit Differentiation with Respect to Time

Differentiate a geometric or algebraic relation with respect to t. Substitute known rates and values to find the unknown rate.

CalculusCommon Core CHA-3.DDERVerified correct ✓

Worked examples

A circular ripple is expanding so that the radius is increasing at 3 cm/s. How fast is the area increasing (in cm²/s) when the radius is 4 cm? Round to 4 decimal places.
Answer: 75.3982
A spherical balloon is being inflated so that its radius grows at 1 cm/s. How fast is the volume increasing (cm³/s) when the radius is 5 cm? Round to 4 decimal places.
Answer: 314.1593

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

Master Related Rates — Implicit Differentiation with Respect to Time

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

Start your free trial 🐾

Build up to this

Implicit Differentiation — Differentiate Implicitly Defined RelationsLaw of Cosines — Solve SAS and SSS Triangles

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