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Math Help - Differentiating and simplifying logarithmic functions.

  1. #1
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    Differentiating and simplifying logarithmic functions.



    For a) I am supposed to use logarithmic differentiation to find the derivative.

    For b) I am supposed to simplify it.

    How would I do these? I have been able to do other hw problems however for these exact ones there are no examples to follow in the book
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  2. #2
    Super Member Quacky's Avatar
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    Re: Differentiating and simplifying logarithmic functions.

    For a)

    Assume we have y=3^x
    Take natural logs of both sides:
    ln(y)=x\cdot{ln(3)}
    Now you can use implicit differentiation on both sides.

    Edit: For you, things aren't *quite* as simple - but using a simple substitution will help put things into a similar form.

    For b)

    (\frac{1}{4})^x=4^{-x}

    16^\frac{x}{2}=(4^2)^{\frac{x}{2}}

    Tidy up with your exponent laws.
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