How do you differentiate #y= log _5 x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Henry W. Oct 26, 2016 #(dy)/(dx)=1/(xln5)# Explanation: #y=log_5x=lnx/ln5->#change of base #=1/(ln5)lnx# #(dy)/(dx)=1/ln5*1/x->1/ln5# is a constant, so we don't change it #=1/(xln5)# 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 24184 views around the world You can reuse this answer Creative Commons License