CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = (2x + 1)⁴, then dy/dx at x = 1 is:
Using the chain rule, the derivative of (2x+1)⁴ is 8(2x+1)³. At x = 1, 2x+1 = 3, so the value is 8 × 27 = 216. Forgetting the inner derivative 2 would give 108, which is wrong.
- A216Correct
- B108
- C54
- D27
Explanation
By the chain rule, dy/dx = 4(2x+1)³·2 = 8(2x+1)³. At x = 1, this is 8×27 = 216. The option 108 results from forgetting the factor 2 only in part (4×27), missing the inner derivative.
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