Answer
$-6x^{-2}$
Work Step by Step
$f(x)=\frac{6}{x}$
$f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$
$f'(x)=\lim\limits_{h \to 0}\frac{(\frac{6}{x+h})-{(\frac{6}{x}})}{h}=\lim\limits_{h \to 0}\frac{(\frac{6x-6(x+h)}{x^2+hx})}{h}=\lim\limits_{h \to 0}\frac{-6h}{h(x^2+hx)}=\lim\limits_{h \to 0}\frac{-6}{x^2+hx}=\frac{-6}{x^2}$$$=-6x^{-2}$$
