What is the key step in a related rates problem?

Differentiating an equation that relates the quantities with respect to time, so each variable’s rate of change appears.

Why is the chain rule needed?

Because each variable depends on time, differentiating with respect to time introduces its rate through the chain rule.

Grade 12 · Mathematics

Related rates

Why it matters

Connected rates of change.

Advanced20m readingPrerequisite: None

What are related rates in calculus?

Short answer

Related rates problems find how fast one quantity changes by relating it to another whose rate is known. You write an equation linking the variables, differentiate both sides with respect to time using the chain rule, and solve for the unknown rate. A classic example is finding how fast a ladder’s top slides down a wall as its base is pulled away.

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Frequently asked questions

What is the key step in a related rates problem?: Differentiating an equation that relates the quantities with respect to time, so each variable’s rate of change appears.
Why is the chain rule needed?: Because each variable depends on time, differentiating with respect to time introduces its rate through the chain rule.

What are related rates in calculus?

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Frequently asked questions