ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 238

\[1)\ y = e^{x} - \sin x;\]

\[y^{'}(x) = e^{x} - \cos x.\]

\[2)\ y = \cos x - tg\ x;\]

\[y^{'}(x) = - \sin x - \frac{1}{\cos^{2}x}.\]

\[3)\ y = ctg\ x - \sqrt[3]{x};\]

\[y^{'}(x) = - \frac{1}{\sin^{2}x} - \frac{1}{3}x^{- \frac{2}{3}}.\]

\[4)\ y = 6x^{4} - 9e^{x};\]

\[y^{'}(x) = 6 \bullet 4x^{3} - 9e^{x};\]

\[y^{'}(x) = 24x^{3} - 9e^{x}.\]

\[5)\ y = \frac{5}{x} + 4e^{x};\]

\[y^{'}(x) = 5 \bullet \left( - \frac{1}{x^{2}} \right) + 4e^{x} =\]

\[= - \frac{5}{x^{2}} + 4e^{x}.\]

\[6)\ y = \frac{1}{3x^{3}} + \frac{1}{2}\ln x;\]

\[y^{'}(x) = \frac{1}{3} \bullet ( - 3) \bullet x^{- 4} + \frac{1}{2} \bullet \frac{1}{x} =\]

\[= - \frac{1}{x^{4}} + \frac{1}{2x}.\]