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 1546 views around the world You can reuse this answer Creative Commons License