Let,
\(f(x)=\sqrt{4-x}\)
∴ \(f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}\)
\(=\lim\limits_{h \to 0}\frac{\sqrt{4-(x+h)}-\sqrt{4-x}}{h}\)
\(=\lim\limits_{h \to 0}\frac{[\sqrt{4-(x+h)}-\sqrt{4-x}][\sqrt{4-(x+h)}+\sqrt{4-x}]}{[h\sqrt{4-(x+h)}+\sqrt{4-x}]}\)
\(=\lim\limits_{h \to 0}\frac{[{4-(x+h)}]-(4-x)}{h[\sqrt{4-(x+h)}+\sqrt{4-x}]}\)
\(=\lim\limits_{h \to 0}\frac{-h}{h\sqrt{4-(x+h)}+\sqrt{4-x}}\)
\(=\lim\limits_{h \to 0}\frac{1}{\sqrt{4-(x+h)}+\sqrt{4-x}}\)
= \(-\frac{1}{2\sqrt{4-x}}\)
