Question

find the third derivative of the given function.

$f(x)=\frac{8}{x^{2}}$

$f(x)=square$

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Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{8}{x^{2}}$ as $f(x) = 8x^{-2}$.

Step2: Find the first - derivative

Using the power rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$, we have $f'(x)=8\times(-2)x^{-2 - 1}=-16x^{-3}$.

Step3: Find the second - derivative

Differentiate $f'(x)$ again. $f''(x)=-16\times(-3)x^{-3 - 1}=48x^{-4}$.

Step4: Find the third - derivative

Differentiate $f''(x)$ one more time. $f'''(x)=48\times(-4)x^{-4 - 1}=-192x^{-5}=-\frac{192}{x^{5}}$.

Answer:

$-\frac{192}{x^{5}}$