How do I use the limit definition of derivative to find f'(x) for f(x)=c ? Calculus Derivatives Limit Definition of Derivative 1 Answer Wataru Sep 20, 2014 f(x)=c is a constant function, so its value stays the same regardless of the x-value. In particular, f(x+h)=c. By the definition of the derivative, f'(x)=lim_{h to 0}{f(x+h)-f(x)}/h =lim_{h to 0}{c-c}/{h} =lim_{h to 0}0 =0 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 us the Limit definition of derivative on f(x)= 1/x? See all questions in Limit Definition of Derivative Impact of this question 8096 views around the world You can reuse this answer Creative Commons License