The chain rule allows functions that are composed of one another to be differentiated. For a function y(u(x)), where y is dependent on u and u is dependent on x, the chain rule defines the rate of change in y with respect to x as the rate of change in y with respect to u times the rate of change in u with respect to x: , in Leibnitz notation. More generally, for two functions f(x) and g(x) constituting the compound function F(x), both of which are differentiable, the derivative of F(x) is . The chain rule can be applied to any number of compounded functions, as needed.
A 727 jet needs to attain a speed of 200 mph to take off. If it can accelerate from 0 to 200 mph in 30 seconds, how long must the runway be? (Assume constant acceleration.)
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