What is the derivative of #f(x)=ln(xsinx)#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions with Base e 1 Answer VinÃcius Ferraz Dec 8, 2015 #f'(x) = 1/x + cot x# Explanation: #f = ln (uv)# #f' = 1/(uv) * (u'v + uv')# #u = x Rightarrow u' = 1# #v = sin x Rightarrow v' = cos x# #f' = (sin x + x cos x) / (x sin x)# 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 3423 views around the world You can reuse this answer Creative Commons License