How do you differentiate #y = ln ((x^2+1)^5 / sqrt(1-x)) #? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer A. S. Adikesavan Sep 16, 2016 #(1+20x-19x^2)/(2(1-x+x^2+x^3))# Explanation: Using #ln(a^n)=nln a and ln(a/b)=lna-ln b and (ln u)'=1/u u'# #y'=5 ln ( 1 + x^2 )-1/2 ln(1- x)#. So, #y'=5/(1+x^2)(1+x^2)'-(1/2)1/(1-x)(1-x)'# #=(10x)/(1+x^2)+1/(2(1-x))# #=(1+20x-19x^2)/(2(1-x+x^2+x^3))# 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 1770 views around the world You can reuse this answer Creative Commons License