(c) if y = \\frac{1}{x^{3}}, find dy/dx.\ndy/dx = □
(c) if y = \\frac{1}{x^{3}}, find dy/dx.\ndy/dx = □
Answer
Explanation:
Step1: Rewrite the function
Rewrite $y = \frac{1}{x^{3}}$ as $y=x^{- 3}$.
Step2: Apply power - rule for differentiation
The power - rule states that if $y = x^{n}$, then $\frac{dy}{dx}=nx^{n - 1}$. Here $n=-3$. So, $\frac{dy}{dx}=-3x^{-3 - 1}$.
Step3: Simplify the result
$\frac{dy}{dx}=-3x^{-4}=-\frac{3}{x^{4}}$.
Answer:
$-\frac{3}{x^{4}}$