How do you find f'(x) using the definition of a derivative for #f(x)= 5x + 9 # at x=2? Calculus Derivatives Limit Definition of Derivative 1 Answer Sasha P. Oct 18, 2015 See the explanation. Explanation: #f'(x)=lim_(h->0) (f(x+h)-f(x))/h# #f'(x)=lim_(h->0) (5(x+h)+9-(5x+9))/h# #f'(x)=lim_(h->0) (5x+5h+9-5x-9)/h# #f'(x)=lim_(h->0) (5h)/h=lim_(h->0) 5 = 5# #f'(x)=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 2870 views around the world You can reuse this answer Creative Commons License