proof of the derivative of a constant dcdx 0it

Question

Proof of the Derivative of a Constant: d(c)/dx = 0

It is very easy to prove by using the definition of the derivative therefore define, f(x) = c and the utilize the definition of the derivative.

 f'(x) = lim_h→0 (f(x +h) - f(x))/h

 = lim_h→0 (c - c)/h

= lim_h→0 0 = 0