Let y - e 2 x- T hen d 2 y - d x 2 d 2 x - dy 2 is -A- 1 B- e-2 x- 2 e-2 xD- -2 e-2 x

The correct option is D ∴dy/dx=2e^2x and d^2y/dx^2=4e^2x dx/dy=1/2e^2x=1/2y ∴d^2x/dy^2= 1/2y^2= 1/2e^ 4x ∴d^2y/dx^2.dx^2/dy^2=4.e^2x.( e^ 2x/2e^2x )= 2e^ 2x ...

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Byju's Answer

Standard XII

Physics

Definite Integrals

Let y = e 2 x...

Question

$L e t y = e^{2 x} . T h e n (\frac{d^{2} y}{d x^{2}}) (\frac{d^{2} x}{d y^{2}}) i s :$

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Solution

The correct option is D
$∴ \frac{d y}{d x} = 2 e^{2 x} a n d \frac{d^{2} y}{d x^{2}} = 4 e^{2 x} \frac{d x}{d y} = \frac{1}{2 e^{2 x}} = \frac{1}{2 y} ∴ \frac{d^{2} x}{d y^{2}} = - \frac{1}{2 y^{2}} = - \frac{1}{2} e^{- 4 x} ∴ \frac{d^{2} y}{d x^{2}} . \frac{d x^{2}}{d y^{2}} = 4. e^{2 x} . (\frac{- e^{- 2 x}}{2 e^{2 x}}) = - 2 e^{- 2 x}$

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Let y=e2x. Then (d2ydx2)(d2xdy2)is:

The correct option is D ∴dydx=2e2x and d2ydx2=4e2xdxdy=12e2x=12y∴d2xdy2=−12y2=−12e−4x∴d2ydx2.dx2dy2=4.e2x.(−e−2x2e2x)=−2e−2x

$L e t y = e^{2 x} . T h e n (\frac{d^{2} y}{d x^{2}}) (\frac{d^{2} x}{d y^{2}}) i s :$