Answer
\[ = \frac{{ - 2}}{{\,\left( {x + h} \right)x}}\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = \frac{2}{x} \hfill \\
\hfill \\
Use{\text{ }}the{\text{ }}definition{\text{ }}of{\text{ }}derivative \hfill \\
\hfill \\
\frac{{f\,\left( {x + h} \right) - f\,\left( x \right)}}{h} = \frac{{\frac{2}{{x + h}} - \frac{2}{x}}}{h} \hfill \\
\hfill \\
combine\,\,fractions \hfill \\
\hfill \\
= \frac{{\frac{{2x - 2\,\left( {x + h} \right)}}{{\,\left( {x + h} \right)x}}}}{h} \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
= \frac{{\frac{{2x - 2x - 2h}}{{\,\left( {x + h} \right)x}}}}{h} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= \frac{{\frac{{ - 2h}}{{\,\left( {x + h} \right)x}}}}{h} \hfill \\
\hfill \\
= \frac{{ - 2h}}{{\,\left( {x + h} \right)xh}} \hfill \\
\hfill \\
= \frac{{ - 2}}{{\,\left( {x + h} \right)x}} \hfill \\
\end{gathered} \]
