CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = (3x + 2)/(x − 1), then dy/dx at x = 3 is:
Using the quotient rule, the derivative of (3x+2)/(x−1) is −5/(x−1)². At x = 3, (x−1)² equals 4, so the derivative is −5/4. The negative sign arises because the numerator is 3(x−1) − (3x+2).
- A−5/4Correct
- B5/4
- C−5/2
- D−1/4
Explanation
By the quotient rule, dy/dx = [3(x−1) − (3x+2)(1)]/(x−1)² = (−5)/(x−1)². At x = 3 the denominator is 4, so dy/dx = −5/4. The option 5/4 has the wrong sign from reversing the numerator order.
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