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Steps for Related Rates Problems: 1. Figure out what rate you want and what rate you have been given. For example, suppose the question gave you dx dy and asked you to calculate . dt dt 2. Now you need to determine the relationship between the two variables, say, x and y. To do that, reread the problem and/or draw a diagram. 3. Now you have two options: either use implicit differentiation or the chain rule. • Implicit: differentiate your equation from step (2) with respect to t to find the relationship between the rates • dy dx and . dt dt Chain rule: set up an equation which uses the chain rule to calculate the rate you want from the rate you have. For the rates given above, you’d write your equation for y with respect to x to find dy dy dx . Now differentiate = dt dx dt dy . dx 4. Substitute the values into the relationship you found in part 3 and calculate. Done! Example: the ladder problem. A ladder is slipping down a vertical wall. The ladder is 5 m long and the top of it is slipping down the wall at a constant rate of 0.3 m/s. How fast is the bottom of the ladder moving away from the wall when the top of the ladder is 4 m above the ground? (Handwritten solution is available separately.)