Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

find y if y = \\frac{2}{3x^{3}}. y = □

Question

find y if y = \frac{2}{3x^{3}}. y = □

Explanation:

Step1: Rewrite the function

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

Step2: Apply the power - rule for differentiation

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

Step3: Simplify the derivative

$y'=- 2x^{-4}=-\frac{2}{x^{4}}$.

Answer:

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