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 1348 views around the world You can reuse this answer Creative Commons License