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B
−1
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C
2
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D
0
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Solution
The correct option is D0 We have, xey−y=sinx⋯(1)
Differentiating both sides with respect to x, we get ey+x⋅eydydx−dydx=cosx ⇒dydx(xey−1)=cosx−ey ⇒dydx=cosx−eyxey−1
At x=0,y=0[From (1)] ∴dydx∣∣∣(0,0)=1−1−1=0