\require{AMSmath}

Uitwerkingen

Oefening 1

\eqalign{   & f(x) = \frac{{2 + \sqrt x }} {x}  \cr   & f'(x) = \frac{{\frac{1} {{2\sqrt x }} \cdot x - \left( {2 + \sqrt x } \right) \cdot 1}} {{x^2 }}  \cr   & f'(x) = \frac{{\frac{1} {2}\sqrt x  - 2 - \sqrt x }} {{x^2 }}  \cr   & f'(x) = \frac{{ - \frac{1} {2}\sqrt x  - 2}} {{x^2 }}  \cr   & f'(x) = \frac{{ - \sqrt x  - 4}} {{2x^2 }} \cr}

Oefening 2

\eqalign{   & f(x) = \frac{{\sqrt x }} {{x + 1}}  \cr   & f'(x) = \frac{{\frac{1} {{2\sqrt x }}\left( {x + 1} \right) - \sqrt x  \cdot 1}} {{\left( {x + 1} \right)^2 }}  \cr   & f'(x) = \frac{{\frac{1} {{2\sqrt x }}\left( {x + 1} \right) - \sqrt x }} {{\left( {x + 1} \right)^2 }}  \cr   & f'(x) = \frac{{\left( {x + 1} \right) - 2\sqrt x  \cdot \sqrt x }} {{2\sqrt x \left( {x + 1} \right)^2 }}  \cr   & f'(x) = \frac{{x + 1 - 2x}} {{2\sqrt x \left( {x + 1} \right)^2 }}  \cr   & f'(x) = \frac{{ - x + 1}} {{2\sqrt x \left( {x + 1} \right)^2 }} \cr}

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