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Math Help - Help! Test tomorrow.

  1. #1
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    Help! Test tomorrow.

    i have a test tomorrow and i need help with some of the questions on the review. i have like 5 of them. here is the first one.

    Find the derivative of the function y=xTanh^-1(lnx)
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  2. #2
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    Quote Originally Posted by BigPapa View Post
    i have a test tomorrow and i need help with some of the questions on the review. i have like 5 of them. here is the first one.

    Find the derivative of the function y=xTanh^-1(lnx)
    You need to use both the chain rule and the product rule.

    First use the product rule:

    u = x \Rightarrow \frac{du}{dx} = 1.

    v = \tanh^{-1} (\ln x) \Rightarrow \frac{dv}{dx} = ?


    To get \frac{dv}{dx} you need to use the chain rule:

    Let w = \ln x \Rightarrow \frac{dw}{dx} = \frac{1}{x} and v = \tanh^{-1} w.

    Then \frac{dv}{dx} = \frac{dv}{dw} \cdot \frac{dw}{dx} = \, ....


    Now put it all together.
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