Related rates problems ask you to find how fast one quantity changes when it is connected to another quantity that is also changing. The key is to relate the variables with one equation, then differentiate with respect to time.
List the variables in the situation and decide which one is the target rate. Mark any given rates clearly, such as (\frac{dx}{dt}) or (\frac{dr}{dt}).
Use the geometric or physical connection from the problem to create one equation involving the variables. If needed, substitute any fixed values from the moment described.
Differentiate both sides implicitly with respect to (t). Remember that every variable depending on time must be treated as a function of (t), so chain rule factors appear.
Substitute the known values after differentiating, then isolate the requested rate. Simplify the final expression fully.
Make sure the sign makes sense: increasing quantities should usually give positive rates, and decreasing ones negative. Also check units, if they are included.
A good habit is to write the original equation before differentiating and to keep track of which values are rates and which are ordinary measurements at a specific instant.
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