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Multivariable Calculus

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Implicit Function, Phi, as a Solution to Exact Differential Eq

MVCALC-FXODV7

The implicit function:

$$\Phi(x,y) = \sqrt{x^2+1} + \sqrt{y^2+1} + 7$$

...is a solution to which of the following exact differential equations?

A

$\frac{x}{\sqrt{x^2+1}} + \frac{y}{\sqrt{y^2+1}} \frac{dy}{dx} = 7$

B

$\frac{y}{\sqrt{y^2+1}} + \frac{x}{\sqrt{x^2+1}} \frac{dy}{dx} = 0$

C

$\frac{x}{\sqrt{x^2+1}} = \frac{y}{\sqrt{y^2+1}} \frac{dy}{dx}$

D

$\frac{x}{\sqrt{x^2+1}} = - \frac{y}{\sqrt{y^2+1}} \frac{dy}{dx}$

E

None of the Above