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 , applying the chain rule to each variable that depends on . 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.
Practice
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1| # | Title | Difficulty | Tags | |
|---|---|---|---|---|
| 84 | The sliding ladder | Medium |
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| # | Title | Difficulty | |
|---|---|---|---|
| 133100 | Equation (4) is … (on a circle) | Medium | |
| 133107 | (Calculus classic) The bottom of a 10-foot ladder is going away from… | Medium | |
| 133109 | How fast does the level of a Coke go down if you… | Medium | |
| 133099 | At 25 meters/second, does your car turn faster or slower than a… | Medium | |
| 133105 | If a plane follows the curve …, and its ground speed is… | Medium | |
| 133101 | (Small paradox first) The right triangle has | Medium | |
| 133102 | (Even smaller paradox) As … moves up the line, why is … | Medium | |
| 133103 | (Faster than light) The derivative of … in Example 9 is | Medium | |
| 133104 | (Explanation by ID) Light travels from … to … in time … | Medium | |
| 133106 | Problems 21–29 are applications of related rates | Medium | |
| 133108 | The top of the 10-foot ladder can go faster than light | Medium | |
| 133110 | A jet flies at 8 miles up and 560 miles per hour | Medium |