The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Connected rates, signs and small changes
Link rates with the chain rule and keep signs and units.
Recover a length rate from a volume or area rate.
Distinguish an instantaneous rate from an exact finite change.
Use \(\displaystyle \frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{dt}\) at the specified instant. A decreasing quantity has a negative signed rate. Convert units before substitution. In the explicitly tagged small-change applications, \(\Delta y\approx f^{\prime}(x)\Delta x\), not an exact equality.