


Chain RuleChain Rule by decompositionThe Chain Rule applies to any composite function, but we will only deal with composite functions in which the last operation is one of the following: a trigonometric function (sine, cosine, tangent, etc.), exponent, logarithm, natural logarithm and raise to a power Any composite function can be written in the form: y = f(g(x)) = fg(x) This can be decomposed into y = f(u) where u = g(x). The Chain Rule says that the derivative of y with respect to the variable x is given by: The steps are:
ExamplesThis example may help you to follow the chain rule method. We apply the method to some more examples. Now lets start with the function:
ExercisesDifferentiate each of these composite functions with respect to x.
A function can be the composition of several functions in succession. We then have to apply the chain rule several times. ExampleMore Multiple Chain Rule Examples ExercisesDifferentiate each equation.
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