Find the indicated derivative. \[ f^{\prime}(x) \text { if } f(x)=3 x+\frac{5}{x} \] The derivative of the function \( f(x)=3 x+\frac{5}{x} \) is

**Step 1. Rewrite the function** We have \[ f(x)=3x+\frac{5}{x}. \] The term \(\frac{5}{x}\) can be rewritten using exponent notation as \[ \frac{5}{x} = 5x^{-1}. \] So, the function becomes \[ f(x)=3x+5x^{-1}. \] **Step 2. Differentiate term by term** Differentiate \(3x\): \[ \frac{d}{dx}(3x)=3. \] Differentiate \(5x^{-1}\) using the power rule \(\frac{d}{dx}(x^n)=nx^{n-1}\): \[ \frac{d}{dx}(5x^{-1})=5\cdot(-1)x^{-1-1}=-5x^{-2}. \] **Step 3. Combine the results** Thus, the derivative is \[ f^{\prime}(x)=3-5x^{-2}. \] We can also express \(5x^{-2}\) as \(\frac{5}{x^2}\). Therefore, the final answer is \[ f^{\prime}(x)=3-\frac{5}{x^2}. \]