What is the derivative of #y=log_10(2x)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Bdub Mar 31, 2017 see below Explanation: Use the Property #color(red)(d/dx(log_bx)=1/(xln b)# #y=log_10(2x)# #color(blue)(y'=1/(2x ln 10) * 2# #color(blue)(y'=1/(cancel2x ln 10) * cancel2# #color(blue)(y'=1/(xln10)# 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 7682 views around the world You can reuse this answer Creative Commons License