A
$
\begin{array}{l}
f(x) = (x^2 + 2)(2x - 1) \\
f'(x) = 2x(2x - 1) + (x^2 + 2) \cdot 2 \\
f'(x) = 4x^2 - 2x + 2x^2 + 4 \\
f'(x) = 6x^2 - 2x + 4 \\
\end{array}
$
B
$
\begin{array}{l}
h(x) = \left( {2x + 2} \right)^6 \cdot \left( {10 - x} \right)^2 \\
h'(x) = 6\left( {2x + 2} \right)^5 \cdot 2 \cdot \left( {10 - x} \right)^2 + \left( {2x + 2} \right)^6 \cdot 2\left( {10 - x} \right) \cdot - 1 \\
h'(x) = 12\left( {2x + 2} \right)^5 \cdot \left( {10 - x} \right)^2 - 2\left( {2x + 2} \right)^6 \cdot \left( {10 - x} \right) \\
h'(x) = 2\left( {2x + 2} \right)^5 \left( {10 - x} \right)\left( {6\left( {10 - x} \right) - \left( {2x + 2} \right)} \right) \\
h'(x) = 2\left( {2x + 2} \right)^5 \left( {10 - x} \right)\left( {60 - 6x - 2x - 2} \right) \\
h'(x) = 2\left( {2x + 2} \right)^5 \left( {10 - x} \right)\left( {58 - 8x} \right) \\
h'(x) = 128\left( {x + 1} \right)^5 \left( {10 - x} \right)\left( {29 - 4x} \right) \\
\end{array}
$
C
$
\begin{array}{l}
f(x) = \left( {3x^2 + 4x + 2} \right)^6 \\
f'(x) = 6\left( {3x^2 + 4x + 2} \right)^5 \cdot \left( {6x + 4} \right) \\
f'(x) = 12\left( {3x + 2} \right)\left( {3x^2 + 4x + 2} \right)^5 \\
\end{array}
$
D
$
\begin{array}{l}
g(x) = (12 - x)^{32} \\
g'(x) = 32 \cdot (12 - x)^{31} \cdot - 1 \\
g'(x) = - 32 \cdot (12 - x)^{31} \\
g'(x) = 32(x - 12)^{31} \\
\end{array}
$
E
$
\begin{array}{l}
g(x) = \left( {x^2 + 2x + 3} \right)\left( {x^2 - 4x + 8} \right) \\
g'(x) = \left( {2x + 2} \right)\left( {x^2 - 4x + 8} \right) + \left( {x^2 + 2x + 3} \right)\left( {2x - 4} \right) \\
g'(x) = 2x^3 - 8x^2 + 16x + 2x^2 - 8x + 16 + 2x^3 - 4x^2 + 4x^2 - 8x + 6x - 12 \\
g'(x) = 4x^3 - 6x^2 + 6x + 4 \\
\end{array}
$
F
$
\begin{array}{l}
f(x) = - x(5 - x)^4 \\
f'(x) = - 1 \cdot (5 - x)^4 + - x \cdot 4(5 - x)^3 \cdot - 1 \\
f'(x) = \left( {5 - x} \right)^3 \left( { - (5 - x) + 4x} \right) \\
f'(x) = \left( {5 - x} \right)^3 \left( {5x - 5} \right) \\
f'(x) = 5(x - 1)\left( {5 - x} \right)^3 \\
\end{array}
$
