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Multivariable Calculus

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Moderate

Find a Function, Phi (x,y)

MVCALC-LVX4YP

Find a function $\Phi(x,y)$ such that:

$$\Phi_x = \frac{1}{1+x^2}$$
$$\Phi_y = \frac{1}{1+y^2}$$

A

$\Phi(x,y) = y\arctan x$

B

$\Phi(x,y) = x\arctan y$

C

$\Phi(x,y) = \arctan x + \arctan y - 3$

D

$\Phi(x,y) = \ln(1+x^2) + \ln(1+y^2)$

E

$\Phi(x,y) = y\ln(1+x^2) + x\ln(1+y^2)$