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 1681 views around the world You can reuse this answer Creative Commons License