Related rates

In related‑rate problems the quantities change together because they are linked by a geometric relationship. First write an equation that ties the variables (often from a right‑triangle, circle, or similar figure). Then differentiate that equation with respect to time $t$, applying the chain rule to each variable that depends on $t$. This produces an equation involving the unknown rate you seek and the rates that are given. Finally plug in the known values at the instant of interest and solve for the desired rate. The key idea is: differentiate the constraint equation implicitly with respect to time.