question given the function y = 4 / 3x², find dy / dx. express your answer in simplest form without using…

question given the function y = 4 / 3x², find dy / dx. express your answer in simplest form without using negative exponents. answer attempt 2 out of 2 dy / dx = \nsubmit answer \nwatch video \nshow exan

question given the function y = 4 / 3x², find dy / dx. express your answer in simplest form without using negative exponents. answer attempt 2 out of 2 dy / dx = \nsubmit answer \nwatch video \nshow exan

Answer

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{4}{3x^{2}}$ as $y=\frac{4}{3}x^{- 2}$.

Step2: Apply power - rule for differentiation

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

Step3: Simplify the derivative

$\frac{dy}{dx}=-\frac{8}{3}x^{-3}$. Then, rewrite without negative exponents: $\frac{dy}{dx}=-\frac{8}{3x^{3}}$.

Answer:

$-\frac{8}{3x^{3}}$