Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 240

\[1)\ y = x^{2}\cos x;\]

\[y^{'}(x) = 2x \bullet \cos x + x^{2} \bullet \left( - \sin x \right);\]

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

\[2)\ y = x^{3}\ln x;\]

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

\[= x^{2} \bullet \left( 3\ln x + 1 \right).\]

\[3)\ y = 5x\ ctg\ x;\]

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

\[y^{'}(x) = 5\ ctg\ x - \frac{5x}{\sin^{2}x}.\]

\[4)\ y = \sin{2x}\ tg\ x;\]

\[y = 2\sin x\cos xtg\ x = 2\sin^{2}x;\]

\[y^{'}(x) = 2 \bullet 2\sin x \bullet \cos x =\]

\[= 2\sin{2x}.\]

\[5)\ y = e^{- x}\sin x;\]

\[y^{'}(x) = - e^{- x} \bullet \sin x + e^{- x} \bullet \cos x;\]

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

\[6)\ y = e^{x}\cos x;\]

\[y^{'}(x) = e^{x} \bullet \cos x + e^{x} \bullet \left( - \sin x \right);\]

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