If y = 2/x then Y + 1d²y/2dx² =?
- 2(1 + x²)/x³
- x³ - 1/2
- 2 + x/x²
- None of these
Explanation
Given y = 2/x
Let's find the first and second derivatives:
dy/dx = -2/x²
d²y/dx² = 4/x³
Now, let's evaluate y + 1/2 * d²y/dx²:
y + 1/2 * d²y/dx² = 2/x + 1/2 * 4/x³
= 2/x + 2/x³
= (2x² + 2)/x³
= 2(x² + 1)/x³
= 2(1 + x²)/x³
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