Question #9f557 Calculus Basic Differentiation Rules Quotient Rule 1 Answer Jim H Mar 8, 2017 #1/(x-1)-1/x# or (equivalently) #1/(x(x-1))# Explanation: #ln(1-1/x) = ln((x-1)/x) = ln(x-1)-lnx# So the derivative is #1/(x-1)-1/x# which can be written #1/(x(x-1))# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1487 views around the world You can reuse this answer Creative Commons License