How do you find the derivative of #f(x)=1/(x-1) #? Calculus Basic Differentiation Rules Power Rule 1 Answer Sasha P. Oct 23, 2015 #f'(x)=-1/(x-1)^2# Explanation: #f(x)=1/(x-1)=(x-1)^-1# Using the rule: #f(x) =x^n => f'(x)=nx^(n-1)# and chain rule: #f'(x)=-1*(x-1)^-2 * (x-1)' = -(x-1)^-2 = -1/(x-1)^2# #f'(x)=-1/(x-1)^2# Answer link Related questions How do you find the derivative of a polynomial? How do you find the derivative of #y =1/sqrt(x)#? How do you find the derivative of #y =4/sqrt(x)#? How do you find the derivative of #y =sqrt(2x)#? How do you find the derivative of #y =sqrt(3x)#? How do you find the derivative of #y =sqrt(x)#? How do you find the derivative of #y =sqrt(x)# using the definition of derivative? How do you find the derivative of #y =sqrt(3x+1)#? How do you find the derivative of #y =sqrt(9-x)#? How do you find the derivative of #y =sqrt(x-1)#? See all questions in Power Rule Impact of this question 1527 views around the world You can reuse this answer Creative Commons License