Derivative of a constant function

The function $f(x) = -3$ is a constant function, meaning its output never changes regardless of the value of $x$. Since the derivative measures the instantaneous rate of change of a function, and a constant function has a graph that is a horizontal line, its slope is $0$ everywhere.

By the constant rule, $\frac{d}{dx}[c] = 0$ for any constant $c$. Applying this with $c = -3$ gives $f'(x) = 0$.

The derivative would still be zero. No matter what constant value f takes, its graph is a horizontal line with slope zero everywhere. The constant rule tells us the derivative of any constant, regardless of its specific value, is always zero. So changing negative three to negative one hundred does not change the answer at all.