QUESTION IMAGE
Question
find y if y = \frac{2}{3x^{3}}. y = □
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
$y'=- 2x^{-4}=-\frac{2}{x^{4}}$.
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
$-\frac{2}{x^{4}}$