Calculus issue

Let $y=f(x)=\frac{1}{2}$ , then, by first principle: $f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}=\lim_{h\to 0} \frac{\frac{1}{2}-\frac{1}{2}}{h}=0$

The first derivative of constant is $zero$ .

$\frac {d}{dx}$ of a constant $= 0.$

Intuitively, this makes sense: a line whose $y$ value is always the same - in this case, $\frac 12$ - has no rate of change, and thus no slope.