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If xloge(logex)-x^2+y^2=4(ygt0)",then" d...

If `xlog_e(log_ex)-x^2+y^2=4(ygt0)",then" dy//dx" at " x=e` is equal to

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The correct Answer is:
D
`xlog_e(log_e x)-x^2+y^2=4(y > 0)`…(i)
Put `x=e, exx0-e^2+y^2=4 rArr y^2 = 4+e^2 rArr y=sqrt(4+e^2) ( because y > 0)`
Now differentiating (i) both sides w.r.t. x : `log_e (log_e x) + x 1/(log_e x) 1/x -2x + 2y (dy)/(dx)=0`
`rArr (dy)/(dx)"|"_"(x=e)"=(2e-1)/(2sqrt4+e^2)`
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