How do you find f'(x) using the definition of a derivative for #f(x)= x^2 + x#? Calculus Derivatives Limit Definition of Derivative 1 Answer Babette Jun 28, 2016 #f'(x)=2x+1# Explanation: #lim_(hrarr0)[[(x+h)^2+x+h]-[x^2+x]]/h# #lim_(hrarr0)[[x^2+2xh+h^2+x+h]-[x^2+x]]/h# #lim_(hrarr0)[x^2+2xh+h^2+x+h-x^2-x]/h# #lim_(hrarr0)[2xh+h^2+h]/h# #lim_(hrarr0)[h(2x+h+1)]/h# #lim_(hrarr0)2x+h+1=2x+0+1=2x+1# 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 1361 views around the world You can reuse this answer Creative Commons License