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How do I use the limit definition of derivative to find #f'(x)# for #f(x)=c# ?

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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#

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