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Question

Suppose, A=dydx of x2+y2=4 at (2,2),B=dydx of siny+sinx=sinxsiny at (π,π) and C=dydx of 2exy+exeyex=exy+1 at (1,1), then (ABC) has the value equal to .....

A
12
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B
13
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C
1
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D
2
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Solution

The correct option is D 12
A:ddx(x2+y2=4) at (2,2))
2x+2ydydx=0
dydx=xy=22=1
B:ddx(siny+sinx=sinxsiny) at (π,π)
cosydydx+cosx=sinxcosydydx+sinycosx
dydx(cosysinxcosy)=sinycosxcosx
dydx=cosx(siny1)cosy(1sinx)
B=1(01)1(10)=1
C:ddx(2exy+exeyex=exy+1) at (1,1)
[2exy(xdydx+y)]+exeydydx+eyexex=exy+1(xdydx+y)
dydx=yexy+12yexyex+y+ex2xexy+ex+yxexy+1.......... since exey=ex+y
C=e22e1e2+e12e1+e2e2
=e12e1=12
Therefore ABC=12

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