Using the limit definition, how do you differentiate #f(x) = x+3#? Calculus Derivatives Limit Definition of Derivative 1 Answer Trevor Ryan. Nov 5, 2015 #f'(x)=1# Explanation: By definition, #f'(x)=lim_(h->0)(f(x+h)-f(x))/h# #=lim_(h->0)(((x+h)+3)-(x+3))/h# #=lim_(h->0)h/h# #=lim_(h->0)(1)=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 1105 views around the world You can reuse this answer Creative Commons License