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Question

If xyyx=16, then dydx at (2, 2) is

A
– 1
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B
1
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C
none of these
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Solution

The correct option is A – 1
xyyx=16
\Rightarrow y log_e x + x log_e y = 4 log_e 2\)
Now, differentiating both sides w.r.t. x
yx+logexdydx+xydydx+logey.1=0dydx=(logey+yx)(logex+yx)dydx|(2,2)=(loge2+1)(loge2+1)=1

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