ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 833

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\[1)\ f(x) = 2^{x} + e^{x}\]

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

\[= 2^{x} \bullet \ln 2 + e^{x}\]

\[2)\ f(x) = 3^{x} - x^{- 2}\]

\[f^{'}(x) = \left( 3^{x} \right)^{'} - \left( x^{- 2} \right)^{'} =\]

\[= 3^{x} \bullet \ln 3 + 2x^{- 3}\]

\[3)\ f(x) = e^{2x} - x\]

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

\[4)\ f(x) = e^{3x} + 2x^{2}\]

\[f^{'}(x) = \left( e^{3x} \right)^{'} + 2 \bullet \left( x^{2} \right)^{'} =\]

\[= 3e^{3x} + 2 \bullet 2x = 3e^{3x} + 4x\]

\[5)\ f(x) = 3^{x^{2} + 2}\]

\[u = x^{2} + 2\ f(u) = 3^{u}\]

\[f^{'}(x) = \left( x^{2} + 2 \right)^{'} \bullet \left( 3^{u} \right)^{'} =\]

\[= 2x \bullet 3^{u} \bullet \ln 3 = 2x \bullet 3^{x^{2} + 2} \bullet \ln 3.\]