CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
If y = (3x + 2)^4, what is dy/dx at x = 0?
By the chain rule, the derivative of (3x + 2)^4 is 4(3x + 2)^3 multiplied by the inner derivative 3, giving 12(3x + 2)^3. At x = 0 this equals 12 × 8 = 96.
- A32
- B96Correct
- C24
- D8
Explanation
Chain rule: dy/dx = 4(3x + 2)^3 · 3 = 12(3x + 2)^3. At x = 0: 12 × 8 = 96. Option 32 omits the inner derivative 3 (4 × 8).
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