[tex]1)\\y = (2+x) * \sqrt{3-x}\\y'=(2+x)'*\sqrt{3-x} + (2+x) * (\sqrt{3-x})' = \sqrt{3-x}+\frac{2+x}{2\sqrt{3-x}} *(3-x)'=\sqrt{3-x}-\frac{2+x}{2\sqrt{3-x}}=\frac{2*(3-x)-2-x}{2\sqrt{3-x}} = \frac{4-3x\\}{2\sqrt{3-x}}\\2)\\y=\sqrt{x^3+2x-5}\\y' = \frac{1}{2\sqrt{x^3+2x-5}}*(x^3+2x-5)' = \frac{3x^2+2}{2\sqrt{x^3+2x-5}}\\[/tex]

[tex]3)\\y=\frac{\sqrt{9+x^2}}{x}\\y'=\frac{(\sqrt{9+x^2})'*x-(\sqrt{9+x^2})*x'}{x^2}=\frac{\frac{(9+x^2)'*x}{2\sqrt{9+x^2}}-\sqrt{9+x^2}}{x^2}=\frac{1}{x^2}*\frac{2x^2-2(9+x^2}{2\sqrt{9+x^2}}= -\frac{9}{x^2\sqrt{9+x^2}}\\4) \\y=\sin^3{x}\\y' = 3\sin^2{x}*(\sin{x})' =3\sin^2{x}*\cos{x}[/tex]