How do you find f'(x) using the definition of a derivative for #f(x)= 2x^2-x #? Calculus Derivatives Limit Definition of Derivative 1 Answer Sasha P. Sep 27, 2015 #4x-1# See the explanation. Explanation: #f'(x)=lim_(h->0) (f(x+h)-f(x))/h# #lim_(h->0) (2(x+h)^2-(x+h)-(2x^2-x))/h=# #lim_(h->0) (2x^2+4xh+2h^2-x-h-2x^2+x)/h=# #lim_(h->0) (4xh+2h^2-h)/h=lim_(h->0) (4x+2h-1)=4x-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 1304 views around the world You can reuse this answer Creative Commons License