How do you use the limit definition to find the derivative of #y=-1/(x-1)#? Calculus Derivatives Limit Definition of Derivative 1 Answer Eddie Aug 3, 2016 #f'(x) = ( 1)/((x-1)^2 # Explanation: #f'(x) = lim_(h to 0) (f(x+h) - f(x))/(h)# here #f'(x) = lim_(h to 0) 1/h * ( - 1/((x+h)-1) - (- 1/(x-1)))# #f'(x) = lim_(h to 0) 1/h * ( 1/(x-1) - 1/(x+h-1) )# #f'(x) = lim_(h to 0) 1/h * ( (x+h)-1 - (x-1))/((x-1)(x+h-1) # #f'(x) = lim_(h to 0) 1/h * ( h)/((x-1)(x+h-1) # #f'(x) = lim_(h to 0) 1/((x-1)(x+h-1) # #f'(x) = ( 1)/((x-1)(x-1) # #f'(x) = ( 1)/((x-1)^2 # Answer link Related questions What is the limit definition of the derivative of the function #y=f(x)# ? Ho do I use the limit definition of derivative to find #f'(x)# for #f(x)=3x^2+x# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(x+3)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/(1-x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=x^3-2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=1/sqrt(x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=5x-9x^2# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=sqrt(2+6x)# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=mx+b# ? How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ? See all questions in Limit Definition of Derivative Impact of this question 1432 views around the world You can reuse this answer Creative Commons License