Answer:
-1/x²
Step-by-step explanation:
The derivative is the limit of the difference quotient as the interval approaches zero.
[tex]\displaystyle \dfrac{d}{dx}\left(\dfrac{1}{x}\right)=\lim_{h\to0}\dfrac{\dfrac{1}{x+h}-\dfrac{1}{x}}{h}=\lim_{h\to0}\dfrac{x-(x+h)}{h(x)(x+h)}=\lim_{h\to0}\dfrac{-1}{x(x+h)}\\\\=\boxed{-\dfrac{1}{x^2}}[/tex]
