Determine whether the following vector field is conservative on \(\mathbb{R}^2\).
\(F = (e^{5x} \sin (5y), e^{5x} \cos (5y))\)
Is \(F = (e^{5x} \sin (5y), e^{5x} \cos (5y))\) conservative on \(\mathbb{R}^2\)?
A. Yes, because \(\frac{\partial f}{\partial y}\) does not equal \(\frac{\partial g}{\partial x}\).
B. No, because \(\frac{\partial f}{\partial y}\) does not equal \(\frac{\partial g}{\partial x}\).
C. No, because \(\frac{\partial f}{\partial y}\) equals \(\frac{\partial g}{\partial x}\).
D. Yes, because \(\frac{\partial f}{\partial y}\) equals \(\frac{\partial g}{\partial x}\).