How do you use the definition to find the derivative of #3x^2-5x+2#? Calculus Derivatives Limit Definition of Derivative 1 Answer Trevor Ryan. Oct 15, 2015 #6x-5# Explanation: Let #f(x)=3x^2-5x+2# Then #f'(x)= lim_(h->0)(f(x+h)-f(x))/h# #=lim_(h->0)((3(x+h)^2-5(x+h)+2)-(3x^2-5x+2))/h# #=lim_(h->0)(3x^2+6xh+3h^2-5x-5h+2-3x^2+5x-2)/h# #=lim_(h->0)(h(6x+3h-5))/h# #=6x-5# 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 1924 views around the world You can reuse this answer Creative Commons License