Find the Derivative of the Function $f ( x ) = x ^ { 4 } ( 3 + 3 x ) ^ { 3 }$

question 20

Multiple Choice

Find the derivative of the function. $f ( x ) = x ^ { 4 } ( 3 + 3 x ) ^ { 3 }$

• A) \(f ^ { \prime } ( x ) = x ^ { 2 } ( 3 + 3 x ) ^ { 3 } ( 12 + 21 x )\)
• B) \(f ^ { \prime } ( x ) = 3 x ^ { 4 } ( 3 + 3 x ) ^ { 2 } ( 12 + 21 x )\)
• C) \(f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 3 } ( 12 + 21 x )\)
• D) \(f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 2 } ( 12 + 21 x )\)
• E) \(f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 2 } ( 12 + 3 x )\)

---

Definitions:

Maturity Stage

A phase in the product life cycle where growth in sales has started to slow down, and the product is established in the market.

Entrepreneurial Firms

Companies focused on innovation, rapid growth, and high risk, often in emerging industries or markets.

Growth

The process of increasing in size, number, value, or strength, often used in contexts of individual development, economic progress, or business expansion.

Takeoff

In business, refers to the phase where a product or company experiences rapid growth after initial establishment. In aviation, it describes the act of an aircraft becoming airborne.