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Question

If xy=exy, then the value of dydx at x=e is

A
1
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B
-1
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C
14
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D
34
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Solution

The correct option is C 14
Given that
xy=exyTaking log both sides with base e, we gety log x=xyy(1+log x)=xy=x1+log xDifferentiating w.r.t. x both sides, we getdydx=(1+log x)1x1x(1+log x)2dydx=1+log x1(1+log x)2dydx=log x(1+log x)2At x=e(dydx)x=e=log e(1+log e)2=14

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