Question

If $y = \frac{A}{x} + Bx^{2}$ , then $x^{2} \frac{d^{2}y}{dx^{2}} = $

• A. $2y$
• B. $y^2$
• C. $y^3$
• D. $y^4$

Answer 1

Answer: (A)

Given, $y=\frac{A}{x}+B x^{2}$
On differentiating, w.r.t. $x$, we get
$\frac{d y}{d x}=-\frac{A}{x^{2}}+2 B x$
Again differentiating, we get
$ \frac{d^{2} y}{d x^{2}} =+\frac{2 A}{x^{3}}+2 B$
$\therefore x^{2} \frac{d^{2} y}{d x^{2}} =\frac{2 A}{x}+2 B x^{2}$
$=2 y$