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Masja [62]
3 years ago
6

Find DY divided by DX by implicit differentiation y=sinxy 

Mathematics
1 answer:
amm18123 years ago
6 0

Answer:

Step-by-step explanation:

y = sin(xy)\\\frac{d}{dx}y=cos(xy)(\frac{d}{dx}(xy))\\  \frac{d}{dx}y = cos(xy)(y + x*\frac{d}{dx}y)\\ write \: \frac{d}{dx}y \: as\:y'\\y' = cos(xy)(y+xy')\\y' = ycos(xy) + xy'cos(xy) \\y'-xy'cos(xy) = ycos(xy)\\y'(1-xcos(xy)) = ycos(xy)\\\\y' = \frac{ycos(xy)}{1-xcos(xy)}

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