How do you find the derivative of #g(x) = −2/(x + 1)# using the limit definition? Calculus Derivatives Limit Definition of Derivative 1 Answer Euan S. Aug 13, 2016 #=2/(x+1)^2# Explanation: #f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h# #=lim_(hrarr0) (-2/(x+h+1) + 2/(x+1))/h# #=lim_(hrarr0)((-2(x+1))/((x+h+1)(x+1)) + (2(x+h+1))/((x+h+1)(x+1)))/h# #=lim_(hrarr0)((2h)/((x+h+1)(x+1)))/h = lim_(hrarr0) 2/((x+h+1)(x+1))# #=2/(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 2208 views around the world You can reuse this answer Creative Commons License