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 7860 views around the world You can reuse this answer Creative Commons License