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Math Help - Derivative of log

  1. #1
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    Derivative of log

    Find where y'=0 given that y=10^xlogx-10x
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    Re: Derivative of log

    Quote Originally Posted by loghater View Post
    Find where y'=0 given that y=10^xlogx-10x
    The derivative is y'=10^x\log(10)\log(x)+\frac{10^x}{x}-10.
    The solution by inspection is clear.
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    Re: Derivative of log

    How do you get x? I got to the point where (10^xlogx-10x)/logxln10x=0
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    Re: Derivative of log

    Quote Originally Posted by loghater View Post
    How do you get x? I got to the point where (10^xlogx-10x)/logxln10x=0
    That derivative is not correct.
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    Re: Derivative of log

    Quote Originally Posted by loghater View Post
    Find where y'=0 given that y=10^xlogx-10x
    Important question- is "log x" the common logarithm (base 10) or the natural logarithm (base e)? Normally, for a calculus problem I would assume natural logarithm, but the presence of "10^x" makes me ask.

    I presume you know that the derivative of -10x is -10.

    10^x log x is a product so use the product rule: (10^x log x)'= (10^x)' log x+ 10^x (log x)'.

    The derivative of 10^x is (10^x)'= (10^x) ln x and the derivative of log x is
    1) 1/(x ln(10)) if it is common logarithm.
    2) 1/x, if it is natural logarithm.
    Last edited by HallsofIvy; April 10th 2012 at 07:55 AM.
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    Re: Derivative of log

    Quote Originally Posted by loghater View Post
    Find where y'=0 given that y=10^xlogx-10x
    As it is written, there is no way to tell whether the original function is \displaystyle \begin{align*} y = 10^x\log{x} - 10x \end{align*} or \displaystyle \begin{align*}  y = 10^{x\log{x}} - 10x\end{align*} or even something else. The OP needs to clarify, and in future, needs to use brackets or at the very least, some space, where they are needed, or even better, to learn some basic LaTeX.
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