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

The correct option is B ( d^2y/dx^2 ) ( dy/dx )^ 3 d^2x/dy^2=d/dy(dx/dy )=d/dx(dx/dy )dx/dy =d/dx(1/dy/dx )dx/dy= 1/(dy/dx )^2.d^2y/dx^2.1/dy/dx= 1/(dy/dx ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Higher Order Derivatives

d2 x/d y2 equ...

Question

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

$- {(\frac{d^{2} y}{d x^{2}})}^{- 1} {(\frac{d y}{d x})}^{- 3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(\frac{d^{2} y}{d x^{2}}) {(\frac{d y}{d x})}^{- 2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

${(\frac{d^{2} y}{d x^{2}})}^{- 1}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$- (\frac{d^{2} y}{d x^{2}}) {(\frac{d y}{d x})}^{- 3}$

$\frac{d^{2} x}{d y^{2}} = \frac{d}{d y} (\frac{d x}{d y}) = \frac{d}{d x} (\frac{d x}{d y}) \frac{d x}{d y}$
$= \frac{d}{d x} (\frac{1}{\frac{d y}{d x}}) \frac{d x}{d y} = - \frac{1}{{(\frac{d y}{d x})}^{2}} . \frac{d^{2} y}{d x^{2}} . \frac{1}{\frac{d y}{d x}} = - \frac{1}{{(\frac{d y}{d x})}^{3}} \frac{d^{2} y}{d x^{2}}$

Suggest Corrections

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) $\frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} + x y = 0$

Join BYJU'S Learning Program

d2xdy2 equals:

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

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