# Differentiation of logarithmic functions.

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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

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