How do you use the limit definition of the derivative to find the derivative of f(x)=3x^2+3x+3? Calculus Derivatives Limit Definition of Derivative 1 Answer Alberto P. Oct 26, 2016 f^'(x)=lim_(h->0)(f(x+h)-f(x))/h=lim_(h->0)(3*((x+h)^2+(x+h)+1-(x^2+x+1)))/h= =lim_(h->0)(3*(x^2+2xh+h^2+x+h+1-x^2-x-1))/h =lim_(h->0)(3*(2xh+h^2+h))/h =lim_(h->0)3*(2x+h+1)=3(2x+1)=6x+3 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 1552 views around the world You can reuse this answer Creative Commons License