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# Diff from Log

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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
+24430
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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!

Oct 21, 2019
edited by heureka  Oct 21, 2019
edited by heureka  Oct 21, 2019
edited by heureka  Oct 21, 2019
#2
+1

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