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Multivariable Calculus

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Implicit Function is Solution to What Exact Differential Equation

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The implicit function $\Phi(x,y) = 8\sin(xy)+x^2+y^2 = 0$ is a solution to which of the following exact differential equations?

A

$8\cos xy + 2x + (8 \cos xy + 2y) \frac{dy}{dx} = 0$

B

$(8\cos xy + 2x)dx + (8 \cos xy + 2y) dy = 0$

C

$8y\cos xy + (8x\cos xy + 2y) \frac{dy}{dx} = -2x$

D

$8y\cos xy - (8x\cos xy + 2y) \frac{dy}{dx} = 0$

E

None of the Above