Question

find the 2nd derivative of $\frac{3}{x}$

Explanation:

Step1: Rewrite the function

Rewrite $\frac{3}{x}$ as $3x^{- 1}$.

Step2: Find the first - derivative

Use the power rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For $y = 3x^{-1}$, $y^\prime=\frac{d}{dx}(3x^{-1})=-3x^{-2}$.

Step3: Find the second - derivative

Differentiate $y^\prime=-3x^{-2}$ again using the power rule. $y^{\prime\prime}=\frac{d}{dx}(-3x^{-2}) = 6x^{-3}=\frac{6}{x^{3}}$.

Answer:

$\frac{6}{x^{3}}$