If \( y=\frac{x^{2}}{2}+\frac{1}{2} x \sqrt{x^{2}+1}+\log _{e} \sqr...

Описание

If \( y=\frac{x^{2}}{2}+\frac{1}{2} x \sqrt{x^{2}+1}+\log _{e} \sqrt{x+\sqrt{x^{2}+1}} \), then
\( \mathrm{P} \)
(1) \( y^{\prime}=x+\sqrt{x^{2}+1} \)
W.
(2) \( y^{\prime}=\frac{1}{x+\sqrt{x^{2}+1}} \)
(3) \( 2 y=x y^{\prime}+\log _{e} y^{\prime} \)
(4) \( 2 y=x y^{\prime}-\log _{e} y^{\prime} \)
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