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Question

Let y=e2x, then d2ydx2d2xdy2 is


A

1

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B

e-2x

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C

-2e-2x

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D

y=e2x

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Solution

The correct option is C

-2e-2x


Find the value of d2ydx2d2xdy2:

Given,y=e2x(i)

Differentiating equation (i) w.r.t.'x'

dydx=e2x.2

Again differentiating w.r.t.'x'

d2ydx2=2e2x.2=4e2x(ii)

Differentiating equation (i) w.r.t.'y'

1=2e2xdxdydxdy=12e2x=12yy=e2x

Again differentiating w.r.t.'y'

d2xdy2=12-1y-2=-12e2x-2y=e2x=-12e4x(iii)

Calculate d2ydx2d2xdy2

Substitute (ii) and (iii)

d2ydx2d2xdy2=4e2x×-12e4x=-2e-2x

Hence, the correct answer is option (C)


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