\require{AMSmath}


Uitwerkingen

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}


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