Answer
$-2x $
Work Step by Step
$\frac{dy}{dx}=\lim\limits_{h\to 0}\frac{f(x+h)-f(x)}{h}$
$=\lim\limits_{h \to 0}\frac{[4-(x+h)^{2}]-(4-x^{2})}{h}$
$=\lim\limits_{h \to 0}\frac{x^{2}-(x+h)^{2}}{h}$
$=\lim\limits_{h \to 0}\frac{x^{2}-x^{2}-h^{2}-2xh}{h}$
$\lim\limits_{h \to 0}(-h-2x)=-2x $
