Вычисление производных.[latex]lg ^{2} \sqrt{x} [/latex][latex]ln (x+ \sqrt{1+ x^{2} } )[/latex][latex]log_5 \sqrt{2 x^{2} -3x+4} [/latex]

[latex]y=lg^2\sqrt{x}\\\\y'=2lg\sqrt{x}\cdot \frac{1}{\sqrt{x}ln10}\cdot \frac{1}{2\sqrt{x}}=\frac{lg\sqrt{x}}{xln10}\\\\\\y=ln(x+\sqrt{1+x^2})\\\\y'=\frac{1}{x+\sqrt{1+x^2}}\cdot (1+\frac{1}{2\sqrt{1+x^2}}\cdot 2x)}=\frac{1}{x+\sqrt{1+x^2}}\cdot \frac{\sqrt{1+x^2}+x}{\sqrt{1+x^2}}=\frac{1}{\sqrt{1+x^2}}\\\\\\y=log_5\sqrt{2x^2-3x+4}\\\\y'=\frac{1}{\sqrt{2x^2-3x+4}\, \cdot ln5}\cdot \frac{1}{2\sqrt{2x^2-3x+4}}\cdot (4x-3)=\frac{4x-3}{2ln5(2x^2-3x+4)}[/latex]