I was just thinking about the question and googled it but couldn't get anything, is it zero because its a constant function or it is anything more complicated??
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$\begingroup$$$f'(x)=\lim_{h\to 0}\dfrac{f(x+h)-f(x)}h=\lim_{h\to0}\dfrac0h=0.$$
Geometrically speaking, the graph of $f\colon x\mapsto0$ is a horizontal line, so its slope at each point is zero, hence its derivative is equal to zero everywhere. From another perspective, $f\colon x\mapsto0$ is a constant function, it doesn't vary, so its rate of change is zero.
$\endgroup$ $\begingroup$The point of differentiation is to find the rate of change of a quantity, physically. Since zero never changes, it is clearly a constant. So its derivative must be zero.
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