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Math Help - Differentiation

  1. #1
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    Differentiation

    need help differentiating (6e^2x-x)^3




    also finding the first and second derivatives for f(x)=1-2x over e^x

    I used the general power rule to get -2(e^x)-e^x(1-2x) over (ex)^2, but I dont know if thats right and don't know where to go from there to get the second derivative.


    Also for this problem e^(x^2+9)times e^(6x)=1 can I just drop the base's because there the same? how would you solve this?

    Any help is greatly appreciated thanks.
    Last edited by mr fantastic; April 18th 2010 at 07:01 PM. Reason: Re-titled post
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  2. #2
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    Quote Originally Posted by mike21 View Post
    need help differentiating (6e^2x-x)^3

    chain rule ...

    \textcolor{red}{3(6e^{2x} - x)^2 \cdot (12e^{2x} - 1)}

    also finding the first and second derivatives for f(x)=1-2x over e^x

    quotient rule ...

    \textcolor{red}{f'(x) = \frac{e^x(-2) - (1-2x)e^x}{e^{2x}}}<br />

    \textcolor{red}{f'(x) = \frac{e^x[-2 - (1-2x)]}{e^{2x}}}

    \textcolor{red}{f'(x) = \frac{e^x(2x-3)}{e^{2x}} = \frac{2x-3}{e^x}}

    now do the quotient rule again

    Also for this problem e^(x^2+9)times e^(6x)=1 can I just drop the base's because there the same? how would you solve this?

    \textcolor{red}{e^{x^2+9} \cdot e^{6x} = e^{x^2+6x+9} = e^{(x+3)^2} = 1}

    \textcolor{red}{(x+3)^2 = 0}
    ...
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