find the third derivative of the given function.\n\n$f(x)=\frac{8}{x^{2}}$\n\n$f(x)=square$\n\nresources\nrea…
find the third derivative of the given function.\n\n$f(x)=\frac{8}{x^{2}}$\n\n$f(x)=square$\n\nresources\nread it watch it
Answer
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:
$-\frac{192}{x^{5}}$