Question

given the function $f(x)=\frac{2}{x}$, find $f(x)$. express your answer in simplest form without using negative exponents.

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{2}{x}$ as $f(x) = 2x^{-1}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. Here, $a = 2$ and $n=-1$. So, $f'(x)=2\times(-1)x^{-1 - 1}=-2x^{-2}$.

Step3: Eliminate negative exponents

We know that $x^{-2}=\frac{1}{x^{2}}$, so $f'(x)=-\frac{2}{x^{2}}$.

Answer:

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