How do you find the derivative of f(x)= 2/x?

Apr 12, 2018

$f ' \left(x\right) = - \frac{2}{x} ^ 2$

Explanation:

The Quotient Rule isn't really needed here, we may rewrite with negative exponents and apply the rule.

$\frac{2}{x} = 2 {x}^{-} 1$

$\frac{d}{\mathrm{dx}} \left(2 {x}^{-} 1\right) = - 2 {x}^{-} 2 = - \frac{2}{x} ^ 2$

$f ' \left(x\right) = - \frac{2}{x} ^ 2$