If \( e^{y}+x y=e \), the ordered pair \( \left(\frac{d y}{d x}, \f...
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If \( e^{y}+x y=e \), the ordered pair \( \left(\frac{d y}{d x}, \frac{d^{2} y}{d^{2}}\right) \) at \( x=0 \) is equal
\( \mathrm{P} \) to :
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(a) \( \left(-\frac{1}{\mathrm{e}}, \frac{1}{\mathrm{e}^{2}}\right) \)
(b) \( \left(\frac{1}{\mathrm{e}}, \frac{1}{\mathrm{e}^{2}}\right) \)
(c) \( \left(\frac{1}{\mathrm{e}},-\frac{1}{\mathrm{e}^{2}}\right) \)
(d) \( \left(-\frac{1}{\mathrm{e}},-\frac{1}{\mathrm{e}^{2}}\right) \)
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