CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
If y = log(x² + 1) (natural logarithm), then dy/dx at x = 2 is:
Differentiating log(x²+1) gives 2x/(x²+1) by the chain rule. At x = 2, the value is 4/5. The derivative of the inner function x²+1, which is 2x, must multiply 1/(x²+1).
- A2/5
- B4/5Correct
- C1/5
- D4/3
Explanation
By the chain rule, dy/dx = (1/(x²+1))·2x = 2x/(x²+1). At x = 2 this is 4/5. The option 2/5 wrongly uses 1/(x²+1)·x, missing the factor 2 from the derivative of x²; 1/5 omits 2x altogether.
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