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Unformatted text preview: OPMT 5701 Lecture Notes 1 The Chain Rule Of all the basic rules of derivatives, the most challenging one is the chain rule. However, like the other rules, if you break it down to simple steps, it too is quite manageble. There are a couple of approaches to learning the chain rule. Both are equally good, it just comes down to preference. The good news is that once you have mastered the chain rule &combined with the rst ve &you are ready to tackle about 90% of the calculus problems found in business courses (including graduate programs like the MBA!) 1.1 The Rule: Suppose y is a "nested" function of x; where nested mean "a function inside a function". y = f [ g ( x )] where g ( x ) is nested inside f . then the derivative is dy dx = y = f [ g ( x )] & g ( x ) (1) The process is to start with the outside function, taking the derivative of f but leaving g ( x ) inside unchanged. Then nd g and multiply it by f ....
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- Fall '11