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Question

If sin(xy)+yx=x2+y2, find dydx.

A
x3xy2cos(xy)+yx3cos(xy)+xx2y
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B
x3+xy2cos(xy)yx3cos(xy)+x2x2y
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C
2x3xy2cos(xy)+yx3cos(xy)x+x2y
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D
2x3xy2cos(xy)+yx3cos(xy)+x2x2y
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Solution

The correct option is D 2x3xy2cos(xy)+yx3cos(xy)+x2x2y
Differentiating both sides wrt x
cos (xy)[y+xdydx]+1x.dydxyx2=2x+2ydydx
ycos(xy)yx22x=(2yxcos(xy)1x)dydx
dydx=2x3+yx2y(cos(xy))x3cos(xy)+x2x2y

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