Question

given the function $f(x)=\frac{2}{x^{3}}$, find $f(x)$. express your answer in simplest form without using negative exponents.

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{2}{x^{3}}$ as $f(x) = 2x^{- 3}$.

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 $n=-3$. So, $f'(x)=2\times(-3)x^{-3 - 1}$.

Step3: Simplify the derivative

$f'(x)=-6x^{-4}$. Then, rewrite it without negative exponents: $f'(x)=-\frac{6}{x^{4}}$.

Answer:

$-\frac{6}{x^{4}}$