Practice question · Put in order
Order the steps of solving a related-rates problem.
- Differentiate both sides with respect to time
- Write an equation relating the quantities involved
- Apply the chain rule so that every changing variable contributes its own rate
- Substitute the known values and known rates
- Solve for the unknown rate
Hints
- The relating equation must hold at all times, so it is written before anything is differentiated.
- Substituting specific numbers too early freezes the variables and destroys their rates.
Show the answer
- Write an equation relating the quantities involved
- Differentiate both sides with respect to time
- Apply the chain rule so that every changing variable contributes its own rate
- Substitute the known values and known rates
- Solve for the unknown rate
Why
Substituting before differentiating is the fatal shortcut: putting r = 2 into the volume formula first makes V a constant, so dV/dt would come out as 0. Numbers go in only AFTER the differentiation is complete.
Practise Related Rates and Implicit Differentiation
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