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# @$3\displaystyle{ \log \| x+\sqrt{ {x}^{2}+A } \| }$

 $3\displaystyle{{ \left{{ \log \| x+\sqrt{ {x}^{2}+A } \| }\right} }^{\prime }}$ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} x+\sqrt{ {x}^{2}+A } \hspace{2}}{ \( x+\sqrt{ {x}^{2}+A } \) }^{\prime }}$ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} x+\sqrt{ {x}^{2}+A } \hspace{2}} \{ 1+\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}}{ \( {x}^{2}+A \) }^{ - \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} }\cdot \( 2x \) \} }$ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} x+\sqrt{ {x}^{2}+A } \hspace{2}} \( 1+\frac{\hspace{2}x\hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+A } \hspace{2}} \) }$ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} x+\sqrt{ {x}^{2}+A } \hspace{2}}\cdot \frac{\hspace{2} x+\sqrt{ {x}^{2}+A } \hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+A } \hspace{2}}}$ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+A } \hspace{2}}}$

z[>>JeS[>>>>̋̓I>>@$3\displaystyle{ \log \| x+\sqrt{ {x}^{2}+A } \| }$

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