Show from first principles that the derivative of a constant is zero

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asked Oct 10, 2023 124k views

1 Answer

Bicarlsen · Answer 1 · 2023-10-15T13:21:59+0000

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

$\begin{gathered} f^(\prime)(x)=\lim_(h\to0)(f(x+h)-f(x))/(h) \\ f^(\prime)(x)=(c-c)/(h) \\ f^(\prime)(x)=0 \end{gathered}$

Hence proved.