Question

(c) if y = \frac{1}{x^{3}}, find dy/dx.
dy/dx = □

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:

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