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    Chain rule

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    Use Chain rule to solve: y=sin((ln(x^2+e^x)+2)^(1/2))^3.

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    (see the attached solution file)

    First rewrite as so that it is easy to see the use of the Power Rule (remember that really means and that is the same as ). The innermost function in all of this is (it counts as a single function because the result of neither function is being plugged into the other). Set this equal to a convenient letter (I am calling these convenient letters intermediate variables): . The next function out from this is the ln, which is having 2 added to it, so make the assignment . ...

    Solution Summary

    This uses the chain rule to differentiate an equation. The differentiation chain rules are provided.