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Constant derivative rul Proof $\frac{d}{dx}a=0$ , for some constant a. Prerequisites The limit definition of the derivative, $f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$ Proof Let f(x) = a for some constant a. From the limit definition of the derivative: $f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$ $f'(x)=\lim_{h \to 0}\frac{a-a}{h}$ $f'(x) = 0$
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