If `y=a x^(n+1)+b x^(-n)` , then `x^2(d^2y)/(dx^2)=` `(a)n(n-1)y` (b) `n(n+1)y` (c) `n y` (d) `n^2y`

Explanation

To solve the problem, we need to find the expression for \( x^2 \frac{d^2y}{dx^2} \) given that \( y = ax^{n+1} + bx^{-n} \).

### Step 1: Differentiate \( y \) to find \( \frac{dy}{dx} \)

Given:
\[ y = ax^{n+1} + bx^{-n} \]
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