Question

hw 12 - higher order derivatives section 2.
(1 point)
calculate the second and the third derivative of $y = 7x-\frac{3}{x}$.
$y=$
$y=$
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Explanation:

Step1: Rewrite the function

Rewrite $y = 7x-\frac{3}{x}$ as $y = 7x - 3x^{-1}$.

Step2: Find the first - derivative

Using the power rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$, we have $y'=\frac{d}{dx}(7x-3x^{-1})=7+3x^{-2}$.

Step3: Find the second - derivative

Differentiate $y'$ with respect to $x$. $y''=\frac{d}{dx}(7 + 3x^{-2})=-6x^{-3}=-\frac{6}{x^{3}}$.

Step4: Find the third - derivative

Differentiate $y''$ with respect to $x$. $y'''=\frac{d}{dx}(-6x^{-3}) = 18x^{-4}=\frac{18}{x^{4}}$.

Answer:

$y''=-\frac{6}{x^{3}}$
$y'''=\frac{18}{x^{4}}$