If y = (A/x) + Bx2 , then x2 (d2y/dx2) =

Question

If y = (A/x) + Bx2 , then x2 (d2y/dx2) =  (A) 2y (B) y2 (C) y3 (D) y4

Tardigrade Admin · Accepted Answer

Given, y=(A/x)+B x2 On differentiating, w.r.t. x, we get (d y/d x)=-(A/x2)+2 B x Again differentiating, we get (d2 y/d x2) =+(2 A/x3)+2 B ∴ x2 (d2 y/d x2) =(2 A/x)+2 B x2 =2 y

Q. If $y = \frac{A}{x} + B x^{2}$ , then $x^{2} \frac{d ^{2} y}{d x ^{2}} =$

$2 y$

$y^{2}$

$y^{3}$

$y^{4}$

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
$\frac{d ^{2} y}{d x ^{2}} = + \frac{2 A}{x ^{3}} + 2 B$
$∴ x^{2} \frac{d ^{2} y}{d x ^{2}} = \frac{2 A}{x} + 2 B x^{2}$
$= 2 y$

Q. If y=xA​+Bx2 , then x2dx2d2y​=

2y

y2

y3

y4