Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 837

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\[1)\ f(x) = \sin(2x - 1)\]

\[f^{'}(x) = \left( \sin(2x - 1) \right)^{'} =\]

\[= 2\cos{(2x - 1)}\]

\[2)\ f(x) = \cos(x + 2)\]

\[f^{'}(x) = \left( \cos(x + 2) \right)^{'} =\]

\[= - \sin(x + 2)\]

\[3)\ f(x) = \sin(3 - x)\]

\[f^{'}(x) = \left( \sin(3 - x) \right)^{'} =\]

\[= - \cos(3 - x)\]

\[4)\ f(x) = \cos\left( x^{3} \right)\]

\[u = x^{3}\text{\ \ }f(u) = \cos u:\]

\[f^{'}(x) = \left( x^{3} \right)^{'} \bullet \left( \cos u \right)^{'} =\]

\[= 3x^{2} \bullet \left( - \sin u \right) = - 3x^{2} \bullet \sin x^{3}.\]