=for timestamp
Do Feb  3 17:54:23 CET 2005

=head3 36. Hausaufgabe

=head4 Selbstgestellte Aufgaben

=over

=item 4)

M<f(x) = \sqrt{5x}; \Rightarrow f'(x) = \frac{\sqrt{5}}{2\sqrt{x}} =
\frac{\sqrt{5x}}{2x};>

=item 5)

M<f(x) = x \cdot \left(2x^2 + 3\right) = 2x^3 + 3x; \Rightarrow f'(x) = 6x^2 +
3;>

=item 6)

M<f(x) = \dfrac{\sqrt{x}}{x} = \dfrac{x^{\frac{1}{2}}}{x^1} = x^{-\frac{1}{2}};
\Rightarrow f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} =
-\frac{1}{2}\frac{1}{\sqrt{x^3}} = -\frac{1}{2}\frac{\sqrt{x^3}}{x^3};>

=item 7)

M<f(x) = x^m \cdot x^n = x^{m + n}; \Rightarrow f'(x) = \left(m + n\right)x^{m
+ n - 1};>

=back