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Math Help - log derivatives

  1. #1
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    log derivatives

    y = log 10 (x^2 + 6x)

    I'm confused how to proceed here. Can anyone provide a step by step solution?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Archduke01 View Post
    y = log 10 (x^2 + 6x)

    I'm confused how to proceed here. Can anyone provide a step by step solution?
    Since log is of base 10, you can apply the formula \frac{\,d}{\,dx}\left[\log_a u\right] =\frac{1}{u\ln a}\frac{\,du}{\,dx}

    Can you procede?
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  3. #3
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    Quote Originally Posted by Archduke01 View Post
    y = log 10 (x^2 + 6x)

    I'm confused how to proceed here. Can anyone provide a step by step solution?
    The log is to that base 10 correct?

    I'll assume that you know \frac{d}{du}ln(u)=\frac{1}{u}

    log_{10}(x^2+6x)=\frac{ln(x^2+6x)}{ln(10)}

    Since ln(10) is a constant, the derivative is

    \frac{1}{ln(10)}\frac{d}{dx}ln(x^2+6x)

    Use the chain rule to obtain:

    =\frac{2x+6}{ln(10)(x^2+6x)}
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  4. #4
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    NOte that I had to edit my original post from an error. I hope I didn't throw you off.
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  5. #5
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    Quote Originally Posted by adkinsjr View Post

    Since ln(10) is a constant, the derivative is

    \frac{1}{ln(10)}\frac{d}{dx}ln(x^2+6x)
    Thanks for the detailed steps, buddy.

    But if it weren't a constant, what would the derivative be?
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