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If $ y = \log_{10} X + \log_e 10 + \log_x X + \log_{10} 10$, then find $\frac{dy}{dx} $

So I was doing this question and when I got my result it didn't match with the answer given in my book . My book had the answer as $ 1 / (X \log_{10}) $ where as my answer was $ 1/ (X \log_{10} ) + 1 /10 $

I strongly believe that my answer is right but still can be wrong . So can somebody please clarify the answer

Can somebody please edit the question on my behalf

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  • $\begingroup$ Welcome to math stack exchange. What is $log_x x$? $\endgroup$ May 5 '19 at 19:25
  • $\begingroup$ Wait a sec I am editing it $\endgroup$
    – TheChemist
    May 5 '19 at 19:25
  • $\begingroup$ @J.W.Tanner please reply $\endgroup$
    – TheChemist
    May 5 '19 at 19:45
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    $\begingroup$ Please reply to my question: what is $\log_X X$? $\endgroup$ May 5 '19 at 19:54
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$\log_X X=1$, so $ y = \log_{10} X + \log_e 10 + \log_x X + \log_{10} 10 = \log_{10}X + $ constant.

Can you take it from there ?

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