Solve: sinxy = cos(x + y).

1.	Solve: sinxy = cos(x + y).
Answer» Given sin xy = cos(x + y), diff w.r.t x. cos(xy) \(\Big[x\frac{dy}{dx} + y\Big]\) \(\frac{dy}{dx}\)[sin(x + y) + xcos (xy)] = -sin(x + y) – ycos(xy) \(\frac{dy}{dx} = \frac{-\Big[sin(x + y) + cosxy\Big]}{\Big(sin(x + y) + xcosxy\Big)}\)

Answer»

Given sin xy = cos(x + y), diff w.r.t x.

cos(xy) \(\Big[x\frac{dy}{dx} + y\Big]\)

\(\frac{dy}{dx}\)[sin(x + y) + xcos (xy)] = -sin(x + y) – ycos(xy)

\(\frac{dy}{dx} = \frac{-\Big[sin(x + y) + cosxy\Big]}{\Big(sin(x + y) + xcosxy\Big)}\)

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