Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 204

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

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

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

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

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

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

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

\[y^{'}(x) = 3\cos^{2}x \bullet \left( - \sin x \right) =\]

\[= - 3\sin x\cos^{2}x.\]

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

\[y^{'}(x) = 4\sin^{3}x \bullet \cos x.\]

\[5)\ y = e^{2x^{2}};\]

\[y^{'}(x) = 2 \bullet 2x \bullet e^{2x^{2}} = 4xe^{2x^{2}}.\]

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

\[y^{'}(x) = - 4x^{3}e^{- x^{4}}.\]

\[7)\ y = \ln{3x^{4}};\]

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

\[8)\ y = \ln( - 2x);\]

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