CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = (x² + 1)/(x − 1), then dy/dx at x = 2 is:
Applying the quotient rule, dy/dx = [2x(x−1) − (x²+1)]/(x−1)². At x = 2 the numerator is 4 − 5 = −1 and the denominator is 1, so the derivative is −1.
- A−1Correct
- B1
- C5
- D−5
Explanation
Quotient rule: dy/dx = [2x(x−1) − (x²+1)(1)]/(x−1)². At x = 2: numerator = 4·1 − 5 = −1; denominator = 1. So dy/dx = −1. Option 1 results from a sign error in the numerator.
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