Question

given the function $f(x)=\frac{3}{x^{4}}$, find $f(x)$. express your answer in simplest form without using negative exponents.

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{3}{x^{4}}$ as $f(x)=3x^{- 4}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y'=anx^{n - 1}$. Here, $a = 3$ and $n=-4$. So $f'(x)=3\times(-4)x^{-4 - 1}$.

Step3: Simplify the derivative

$f'(x)=-12x^{-5}$. Then, rewrite without negative exponents: $f'(x)=-\frac{12}{x^{5}}$.

Answer:

$-\frac{12}{x^{5}}$