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Find the derivative with step by step as simple 

The function given in the image is:

\[ f(x) = x^3 + \frac{4}{x} \]

We need to find the derivative of this function. Let's break this down into steps:

1. **Apply the Power Rule to \(x^3\):**
   \[ \frac{d}{dx}x^3 = 3x^2 \]

2. **Apply the Power Rule to \(\frac{4}{x}\), which can be rewritten as \(4x^{-1}\):**
   \[ \frac{d}{dx}(4x^{-1}) = 4 \cdot (-1) \cdot x^{-2} = -4x^{-2} \]
   This simplifies to:
   \[ -4x^{-2} = -\frac{4}{x^2} \]

Combining these results, the derivative of the function \(f(x)\) is:

\[ f'(x) = 3x^2 - \frac{4}{x^2} \]

Would you like further details on the rules used or how they apply? Here are some related questions you might consider:

1. How can you apply the power rule to more complex expressions?
2. What are the general rules for finding derivatives of rational functions?
3. Can you explain how to derive trigonometric functions?
4. What is the chain rule and how is it used in calculus?
5. How would you find the second derivative of the given function?

**Tip:** Always simplify expressions before differentiating to make the calculations easier and to avoid common errors.

Find the derivative of f(x) = x^3 + 4/x with step by step solution.

Learn how to find the derivative of f(x) = x^3 + 4/x with a detailed step-by-step explanation. This solution applies the Power Rule and simplifies the result, suitable for students in Grades 11-12 studying calculus.

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