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For y = (x + √(1 + x²))ⁿ, the value of (1 + x²) d²y/dx² + x dy/dx is

1. n²y
2. -n²y
3. -y
4. 2x²y

Correct answer: n²y

Solution

The expression (1 + x²)d²y/dx² + x dy/dx simplifies to n²y due to the properties of the function y and its derivatives, which reflect the structure of the original equation when differentiated appropriately.

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