\ANG{
Berechnen Sie die Ableitung folgender Funktionen.
\begin{enumerate}
\item $f_1(x)=(2x+3)^4(4x^2-6)^7$
\item $f_2(x)=(2x^4-3)^5(3x-4x^5)^4$
\item $f_3(x)=(3x+2)^4\sqrt{1+x^2}$
\item $f_4(x)=(x+2)^2\sqrt{x+1}$
\item $f_5(x)=(x^3-1)^3\sqrt{x^2+x+1}$
\item $\displaystyle f_6(x)=\sqrt{\frac{x+2}{x-2}}$
\item $\displaystyle f_7(x)=\sqrt{\frac{1}{x^2-2}}$
\item $\displaystyle f_8(x)=\frac{x\sqrt{1+x}}{x^2+2}$
\item $\displaystyle f_9(x)=\frac{2x^3\sqrt{1-x}}{3x^2-4}$
\end{enumerate}

}
\LSG{
\begin{enumerate}
\item $f'_1(x)=24\cdot (2x+3)^3(4x^2-6)^6(6x^2+7x-2)$
\item $f'_2(x)=4\cdot (2x^4-3)^4(3x-4x^5)^3(-80x^8+96x^4-9)$
\item $\displaystyle f'_3(x)=\frac{(3x+2)^3(15x^2+2x+12)}{\sqrt{1+x^2}}$
\item $\displaystyle f'_4(x)=\frac{(x+2)\, (5x+6)}{2\sqrt{x+1}}$
\item $\displaystyle f'_5(x)=\frac{(x^3-1)^2(20x^4+19x^3+18x^2-2x-1)}{2\sqrt{x^2+x+1}}$
\item $\displaystyle f'_6(x)=-\frac 2{(x-2)^2}\sqrt{\frac{x-2}{x+2}}$
\item $\displaystyle f'_7(x)=-\frac{x\sqrt{x^2-2}}{(x^2-2)^2}$
\item $\displaystyle
  f'_8(x)=\frac{-x^3-2x^2+6x+4}{2\sqrt{1+x}(x^2+2)^2}=
  \frac{(2-x)(x^{2}+4\,x+2)}{2\sqrt{1+x}(x^2+2)^2}$
\item $\displaystyle f'_9(x)=\frac{x^2\, (-9x^3+6x^2+28x-24)}{(3x^2-4)^2\sqrt{1-x}}$
\end{enumerate}
}
