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    Chain Rule, Leibnitz Notation and Inner and Outer Functions

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    The Chain Rule states how to differentiate composite functions

    If and be differentiable, then the derivative of the composite function is

    In Leibnitz notation, if and , then .
    For example,

    or

    The derivative of the exponential function is

    3. Identify the inner function and the outer function in . Then find the derivative .
    4. Identify the inner function and the outer function in the following: . Then find the derivative .
    5. Identify the inner function and the outer function in the following: . Then find the derivative

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