To show from first principles that the derivative of a constant is zero .
We have to prove that from the first principle the derivative of a constant is zero.
To prove :
If f(x) =c, for some constant c, then f'(x) = 0.
Suppose f(x) = c for some constant c.
Then the derivative of f(x) can be determined as
[tex]\begin{gathered} f^{\prime}(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h} \\ f^{\prime}(x)=\frac{c-c}{h} \\ f^{\prime}(x)=0 \end{gathered}[/tex]Hence proved.
