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Math Help - Please help with a Calc II derivative

  1. #1
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    Please help with a Calc II derivative

    Hi, this was on my last calc test, and I wanted to make sure I understood why I got it wrong.

    Find the derivative of

    (22^x)

    My answer:

    ln(2)22^x

    My guess now that I realize it's wrong:

    ln(4)(4x)

    Thanks!
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Please help with a Calc II derivative

    2^{1+2x}\text{ln}(2)
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  3. #3
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    Re: Please help with a Calc II derivative

    Hello, rocapp!

    This requires some fancy footwork . . .


    \text{Find the derivative of: }\:y \;=\;2^{2^x}

    \text{Take logs: }\:\ln(y) \:=\:\ln\left(2^{2^x}\right) \quad\Rightarrow\quad \ln{y}\;=\;2^x\!\cdot\!\ln 2

    \text{Differentiate implicitly: }\:\frac{1}{y}\!\cdot\!y' \;=\;2^x\!\cdot\!(\ln 2)^2

    \text{Therefore: }\:y' \;=\;y\!\cdot\!2^x\!\cdot\!(\ln2)^2 \quad\Rightarrow\quad y'\;=\;2^{2^x}\!\cdot2^x\!\cdot\!(\ln2)^2
    Last edited by skeeter; September 12th 2012 at 05:12 PM.
    Thanks from MarkFL
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