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Hello, if i want the Differential from "log10(ax)" what happens to the a ? i would guess "1/a*x*ln(10)" but i am not sure because in the diff from "ln(ax)" the a fades away because "a*1/a*X"

 Oct 21, 2019
 #1
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Hello, if i want the Differential from "log10(ax)" what happens to the a ?
i would guess "1/a*x*ln(10)" but i am not sure because in the diff from "ln(ax)" the a fades away because "a*1/a*X"

 

\(\begin{array}{|rcll|} \hline y &=& \log_{10}(ax) \\ y &=& \log_{10}(a)+\log_{10}(x) \\ \hline y' &=& \underbrace{\dfrac{d\ \log_{10}(a) }{dx}}_{=0} + \dfrac{d\ \log_{10}(x) }{dx} \\\\ \mathbf{y'} &=& \mathbf{\dfrac{d\ \log_{10}(x) }{dx}} \\\\ \mathbf{y'} &=& \mathbf{\dfrac{1}{x\ln(10)}} \\ \hline \end{array}\)

 

Corrected. Thank you Guest!

 

laugh

 Oct 21, 2019
edited by heureka  Oct 21, 2019
edited by heureka  Oct 21, 2019
edited by heureka  Oct 21, 2019
 #2
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Last two lines heureka, log is base 10.

Guest Oct 21, 2019
 #3
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Thank you very much!

Guest Oct 21, 2019

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