\ANG{
Berechnen Sie die Ableitungen folgender Funktionen:\\[2mm]
$\D\begin{array}[t]{lll}
{\rm (a)}\D\quad f(x)=\frac{1}{x^{999}}\quad & 
{\rm (b)}\D\quad f(x)=\frac{x}{x-3}\quad & 
{\rm (c)}\D\quad f(x)=\frac{x^2-x}{2\,x-5}\\
 & & \\
{\rm (d)}\D\quad f(x)=\frac{x+3}{7-x^2}\quad & 
{\rm (e)}\D\quad f(x)=\frac{x^2-4}{x+2}\quad & 
{\rm (f)}\D\quad f(x)=\frac{\sin x}{\sqrt x}\\
 & & \\
{\rm (g)}\D\quad f(x)=\frac{x^2\,\sin x}{x-\sqrt x}\quad & 
{\rm (h)}\D\quad f(x)=\frac{x^2-1}{x^{10}}\quad & 
{\rm (i)}\D\quad f(x)=\frac{\tan x}{x^2}
\end{array}$
}
\LSG{
$\D\begin{array}[t]{lll}
(a)\D\quad -999\,x^{-1000}\quad & 
(b)\D\quad -\frac{3}{(x-3)^{2}}\quad & 
(c)\D\quad \frac{2\,x^{2}-10\,x+5}{(2\,x-5)^{2}} \\
 & & \\
(d)\D\quad \frac{x^{2}+6\,x+7}{(7-x^2)^{2}}\quad & 
(e)\D\quad (x-2)'=1\quad & 
(f)\D\quad \frac{2\,x\,\cos x-\sin x}{2\,x\,\sqrt x}\quad \\
 & & \\
\multicolumn{2}{l}{
(g)\D\quad \frac{x\,\sin x\left(3\,x-\frac{5}{2}\sqrt{x}\right)+
                 x^{2}\,(x-\sqrt{x})\cos x}{(x-\sqrt {x})^{2}}\quad} & 
(h)\D\quad \frac{2\,(-5\,x^{3}+x^{2}+5)}{x^{11}}\\
 & & \\
(i)\D\quad \frac{x-\sin 2x}{x^{3}\,\cos^{2}x}\quad & &
\end{array}$
}
