How do you differentiate #y = log_3 [((x+1)/(x-1))^ln3]#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer A. S. Adikesavan Aug 28, 2016 #2/(1-x^2)# Explanation: Use #log_ba=ln a/ln b, ln c^n = n ln c and ln(m/s)=ln m - ln n# Here, #y=log_3[((x+1)/(x-1))^ln 3]# #=ln((x+1)/(x-1))^ln 3/ln 3# #=ln 3 ln[(x+1)/(x-1)]/ln 3# #=ln(x+1)-ln(x-1)# y'=1/(x+1)(x+1)'-1/(x-1)(x-1)'# #=1/(x+1)(1)-1/(x-1)(1)# #=((x-1)-(x+1))/((x+1)(x-1))# #=2/(1-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 2591 views around the world You can reuse this answer Creative Commons License