Question

question given the function f(x)= -\frac{1}{2x^{3}}, find f(x). express your answer in simplest form without using negative exponents. answer attempt 1 out of 2 f(x)=

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=-\frac{1}{2x^{3}}$ as $f(x)=-\frac{1}{2}x^{- 3}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y'=anx^{n - 1}$. Here $a=-\frac{1}{2}$ and $n=-3$. So $f'(x)=-\frac{1}{2}\times(-3)x^{-3 - 1}=\frac{3}{2}x^{-4}$.

Step3: Eliminate negative exponent

Since $x^{-4}=\frac{1}{x^{4}}$, then $f'(x)=\frac{3}{2x^{4}}$.

Answer:

$\frac{3}{2x^{4}}$