If $f(x)=\frac{-3 x^{5}+7 x^{4}-7 x^{3}}{x^{4}}$, find $f^{\prime}(x)$

Step 1 ：We are given the function \(f(x)=\frac{-3 x^{5}+7 x^{4}-7 x^{3}}{x^{4}}\) and asked to find its derivative \(f^{\prime}(x)\).

Step 2 ：We can simplify the function first by dividing each term in the numerator by \(x^4\). This gives us \(f(x) = -3x + 7 - \frac{7}{x}\).

Step 3 ：Now, we can find the derivative of the simplified function using the power rule and the quotient rule.

Step 4 ：The derivative of \(-3x\) is \(-3\), the derivative of \(7\) is \(0\), and the derivative of \(-\frac{7}{x}\) is \(\frac{7}{x^2}\).

Step 5 ：Adding these together, we find that the derivative of the function is \(f^{\prime}(x) = -3 + \frac{7}{x^2}\).

Step 6 ：Final Answer: \(f^{\prime}(x) = \boxed{-3 + \frac{7}{x^2}}\)