D2 x-d y2 equals-A- -d2 y-d x2d y-d x-3B- d2 y-d x2-1C- -d2 y-d x2-1d y-d x-3D -d2 y-d x2d y-d x-2

The correct option is A dx/dy= ( dy/dx )^ 1⇒d^2x/dy^2=d/dx ( dy/dx )^ 1.dx/dy= ( dy/dx )^ 2d^2y/dx^2 ( dy/dx )^ 1= ( dy/dx )^ 3 ( d^2y/dx^2 ) ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Derivatives

d2 x/d y2 equ...

Question

$\frac{d^{2} x}{d y^{2}}$ equals:

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Solution

The correct option is D
$\frac{d x}{d y} = {(\frac{d y}{d x})}^{- 1} \Rightarrow \frac{d^{2} x}{d y^{2}} = \frac{d}{d x} {(\frac{d y}{d x})}^{- 1} . \frac{d x}{d y} = - {(\frac{d y}{d x})}^{- 2} \frac{d^{2} y}{d x^{2}} {(\frac{d y}{d x})}^{- 1} = - {(\frac{d y}{d x})}^{- 3} (\frac{d^{2} y}{d x^{2}})$

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Similar questions

$\frac{d^{2} x}{d y^{2}}$ equals:

\frac{d^{2} x}{d y^{2}} e q u a l s

\frac{d^{2} x}{d y^{2}}

equals

\frac{d^{2} x}{d y^{2}} = - \frac{d^{2} y}{d x^{2}} . {(\frac{d x}{d y})}^{3}

Which of the following differential equations has y=x as one of its particular solution?
(a) $\frac{d^{2} y}{d x^{2}} - x^{2} \frac{d y}{d x} + x y = x$
(b) $\frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + x y = x$
(c) $\frac{d^{2} y}{d x^{2}} - x^{2} \frac{d y}{d x} + x y = 0$
(d) $\frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + x y = 0$

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d2xdy2 equals:

The correct option is D dxdy=(dydx)−1⇒d2xdy2=ddx(dydx)−1.dxdy=−(dydx)−2d2ydx2(dydx)−1=−(dydx)−3(d2ydx2)

$\frac{d^{2} x}{d y^{2}}$ equals: