What is the derivative of #y=log_10x/x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Shwetank Mauria Oct 9, 2016 #(dy)/(dx)=log_10e((1-lnx)/x^2)=0.4343((1-lnx))/x^2# Explanation: #y=log_10x/x# can be written as #y=log_10 exxlnx/x# or #y=0.4343xxlnx/x# and using quotient rule Hence #(dy)/(dx)=0.4343xx(x xx1/x-lnx xx1)/x^2# = #0.4343((1-lnx))/x^2# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_2(cos(x))# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 1288 views around the world You can reuse this answer Creative Commons License