Find the third derivative of the given function.
\[
\begin{array}{l}
f(x)=\frac{3}{x^{2}} \\
f^{\prime \prime \prime}(x)=\square
\end{array}
\]
Answer
Final Answer: The third derivative of the function \(f(x)=\frac{3}{x^{2}}\) is \(\boxed{-\frac{72}{x^{5}}}\).
Step 1 ：Given the function \(f(x)=\frac{3}{x^{2}}\), we can rewrite it as \(f(x)=3x^{-2}\) to apply the power rule for differentiation.
Step 2 ：The first derivative of \(f(x)=3x^{-2}\) is \(f'(x)=-6x^{-3}\) or \(f'(x)=-\frac{6}{x^{3}}\).
Step 3 ：The second derivative of \(f'(x)=-\frac{6}{x^{3}}\) is \(f''(x)=18x^{-4}\) or \(f''(x)=\frac{18}{x^{4}}\).
Step 4 ：The third derivative of \(f''(x)=\frac{18}{x^{4}}\) is \(f'''(x)=-72x^{-5}\) or \(f'''(x)=-\frac{72}{x^{5}}\).
Step 5 ：Final Answer: The third derivative of the function \(f(x)=\frac{3}{x^{2}}\) is \(\boxed{-\frac{72}{x^{5}}}\).
