Question

Why is derivative of constant zero?

Answer 1

The explanation for the derivative of constant:

The definition of the derivative is "The instantaneous rate of change in function based on one of its variables, called the differentiation". It's known that the value of a constant can not be changed.

For example:

Find the derivative of $5$. Then,

$\begin{array}{rcl}\frac{d}{dx}\left(5\right)& =& \frac{d}{dx}\left(5x^0\right)\\ & =& 0\left(5x^{0-1}\right)\left[\mathrm{power}\mathrm{rule}:\frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{x}}^{\mathrm{n}}\right)={\mathrm{nx}}^{\mathrm{n}-1}\right]\\ & =& 0\left(5x^{-1}\right)\\ & =& 0\end{array}$

It can be observed from the definition, that the rate of change can be done with a function based on its variable.

Hence,It can be observed that the derivative of the constant term is zero.