How do you find the derivative of g(x) = −2/(x + 1)g(x)=−2x+1 using the limit definition? Calculus Derivatives Limit Definition of Derivative 1 Answer Euan S. Aug 13, 2016 =2/(x+1)^2=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 2304 views around the world You can reuse this answer Creative Commons License