How do you find f'(x) using the definition of a derivative for #f(x)=5.5x^2 - x + 4.2 #? Calculus Derivatives Limit Definition of Derivative 1 Answer Sasha P. Sep 26, 2015 See the explanation. Explanation: #f'(x)=lim_(Deltax->0)(f(x+Deltax)-f(x))/(Deltax)# #lim_(Deltax->0) (5.5(x+Deltax)^2-(x+Deltax)+4.2-(5.5x^2-x+4.2))/(Deltax)# #lim_(Deltax->0) (5.5x^2+11xDeltax+5.5Delta^2x-x-Deltax+4.2-5.5x^2+x-4.2) /(Deltax)# #lim_(Deltax->0) (11xDeltax+5.5Delta^2x-Deltax) /(Deltax)=lim_(Deltax->0) (11x+5.5Deltax-1)# #f'(x)=11x-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 1625 views around the world You can reuse this answer Creative Commons License