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 3033 views around the world You can reuse this answer Creative Commons License