CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If f(x) = 3x² + 5x + 2, find the derivative f'(x).
The derivative of f(x) = 3x² + 5x + 2 is f'(x) = 6x + 5. This follows from applying the power rule to each term: d/dx(3x²) = 6x, d/dx(5x) = 5, and d/dx(2) = 0.
- A6x + 5Correct
- B6x + 2
- C3x + 5
- D6x² + 5
Explanation
Using the power rule for differentiation: the derivative of 3x² is 2·3x = 6x, the derivative of 5x is 5, and the derivative of the constant 2 is 0. Therefore, f'(x) = 6x + 5. The distractor 6x + 2 incorrectly treats the constant.
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