How do you find the derivative of #5^x log_5 x#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Shwetank Mauria Jun 20, 2016 #(df)/(dx)=5^x/(xln5)+5^xlnx# Explanation: #f(x)=5^xlog_5x=5^xlnx/ln5# Hence #(df)/(dx)=1/ln5[5^x xx1/x+lnx xx ln5xx5^x]# = #5^x/(xln5)+5^xlnx# [As #d/dx(5^x)=d/dxe^(ln5^x)=d/dxe^(xln5)=ln5e^(xln5)=ln5xx5^x#) 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 1316 views around the world You can reuse this answer Creative Commons License