If $f(x)=3+\frac{6}{x}+\frac{2}{x^{2}}$, find $f^{\prime}(x)$ Find $f^{\prime}(4)$. Find $f^{\prime \prime}(x)$. Find $f^{\prime \prime}(4)$

Step 1 ：Given the function \(f(x) = 3 + \frac{6}{x} + \frac{2}{x^{2}}\)

Step 2 ：Find the first derivative of the function, \(f^{\prime}(x) = -\frac{6}{x^{2}} - \frac{4}{x^{3}}\)

Step 3 ：Evaluate the first derivative at \(x=4\), \(f^{\prime}(4) = -\frac{7}{16}\)

Step 4 ：Find the second derivative of the function, \(f^{\prime \prime}(x) = \frac{12}{x^{3}} + \frac{12}{x^{4}}\)

Step 5 ：Evaluate the second derivative at \(x=4\), \(f^{\prime \prime}(4) = \frac{15}{64}\)

Step 6 ：\(\boxed{f^{\prime}(4) = -\frac{7}{16}, f^{\prime \prime}(4) = \frac{15}{64}}\)