Question

Can derivatives be zero?

Answer 1

Yes, the derivative $f\text{'}\left(x\right)$ of any function is the rate of change of the value of the function relative to the change of $x$.

So, $f\text{'}\left(cons\tan t\right)=0$ that means the function $f\left(x\right)$ is almost constant around the constant value.

Thus, the derivative of constant function is always zero.