How do you differentiate #y=sqrt(x+1)-ln(1+sqrt(x+1))#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer Cem Sentin Dec 11, 2017 #y'=(sqrt(x+1)-1)/(2x)# Explanation: #y=sqrt(x+1)-ln(1+sqrt(x+1))# #y'=1/[2sqrt(x+1)]-(1/[2sqrt(x+1)])/(1+sqrt(x+1)# =#1/[2sqrt(x+1)]*(1-1/[sqrt(x+1)+1])# =#1/[2sqrt(x+1)]*(sqrt(x+1)/[sqrt(x+1)+1])# =#1/2*1/[sqrt(x+1)+1]# =#(sqrt(x+1)-1)/(2x)# Answer link Related questions What is the derivative of #f(x)=ln(g(x))# ? What is the derivative of #f(x)=ln(x^2+x)# ? What is the derivative of #f(x)=ln(e^x+3)# ? What is the derivative of #f(x)=x*ln(x)# ? What is the derivative of #f(x)=e^(4x)*ln(1-x)# ? What is the derivative of #f(x)=ln(x)/x# ? What is the derivative of #f(x)=ln(cos(x))# ? What is the derivative of #f(x)=ln(tan(x))# ? What is the derivative of #f(x)=sqrt(1+ln(x)# ? What is the derivative of #f(x)=(ln(x))^2# ? See all questions in Differentiating Logarithmic Functions with Base e Impact of this question 1422 views around the world You can reuse this answer Creative Commons License