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B
x3+xy2cos(xy)−yx3cos(xy)+x−2x2y
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C
2x3−xy2cos(xy)+yx3cos(xy)−x+x2y
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D
2x3−xy2cos(xy)+yx3cos(xy)+x−2x2y
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Solution
The correct option is D2x3−xy2cos(xy)+yx3cos(xy)+x−2x2y Differentiating both sides wrt x cos(xy)[y+xdydx]+1x.dydx−yx2=2x+2ydydx ycos(xy)−yx2−2x=(2y−xcos(xy)−1x)dydx dydx=2x3+y−x2y(cos(xy))x3cos(xy)+x−2x2y