CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = log(x² + 3x), where log is the natural logarithm, then dy/dx at x = 1 is:
The derivative of log(x² + 3x) is (2x + 3)/(x² + 3x). At x = 1 the numerator is 5 and the denominator is 4, so the value is 5/4.
- A5/4Correct
- B5/2
- C1/4
- D5
Explanation
Using the chain rule, dy/dx = (2x + 3)/(x² + 3x). At x = 1 this is 5/4. Option 5/2 results from the wrong denominator 2, and 5 results from ignoring the denominator.
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