How do you find the f'(x) using the formal definition of a derivative if #f(x)= 2x^2 - 3x+4#? Calculus Derivatives Limit Definition of Derivative 1 Answer Alan P. · Antoine Apr 12, 2015 #f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h# For #f(x) = 2x^2-3x+4# this becomes #f'(x)# #= lim_(hrarr0)((2(x+h)^2 -3(x+h) +4) - (2x^2 -3x +4))/h# #= lim_(hrarr0) (4xh + h^2-3h)/h# #=lim_(hrarr0) (4x +h -3)# #= 4x-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 3712 views around the world You can reuse this answer Creative Commons License