What is the derivative of #y=ln sqrt(x+1)^5/sqrt(x+2)^20#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Cem Sentin Dec 14, 2017 #y'=5/[(2x+2)*(x+2)^10]-(25Ln(x+1))/(x+2)^11# Explanation: #y=Ln(sqrt(x+1)^5)/(sqrt(x+2)^20)# =#5/2Ln(x+1)/(x+2)^10# #y*(x+2)^10=5/2*Ln(x+1)# #y'(x+2)^10+10y*(x+2)^9=5/(2x+2)# #y'(x+2)^10=5/(2x+2)-10y*(x+2)^9# #y'=5/[(2x+2)*(x+2)^10]-(10y)/(x+2)# #y'=5/[(2x+2)*(x+2)^10]-10/(x+2)*5/2Ln(x+1)/(x+2)^10# #y'=5/[(2x+2)*(x+2)^10]-(25Ln(x+1))/(x+2)^11# 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 2934 views around the world You can reuse this answer Creative Commons License