\ANG{
Berechne die Ableitung folgender Funktionen:\\[2mm]
\begin{tabular}[t]{lll}
(a)\quad$\D f(x)=x\e^{x}$\qquad&
(b)\quad$\D g(x)=\e^{-x^{2}}$\qquad&
(c)\quad$\D h(x)=x\e^{-x^{2}}$\\[2mm]
(d)\quad$\D k(x)=\frac{\e^{x}}{x}$\qquad&
(e)\quad$\D r(x)=x^{2}\e^{-x}$\qquad&
(f)\quad$\D s(x)=x^{2}\e^{-x^{2}}$\\[3mm]
(g)\quad$\D t(x)=\e^{-x}\sin x$\qquad&
(h)\quad$\D u(x)=\e^{\sin x}$\qquad&
(i)\quad$\D v(x)=\sin\left(\e^{x}\right)$
\end{tabular}
} 
\LSG{
\begin{enumerate}
\item $\D f'(x)=\e^{x}+x\e^{x}=(1+x)\e^{x}$
\item $\D g'(x)=-2x\e^{-x^{2}}$
\item $\D h'(x)=\e^{-x^{2}}-2x^{2}\e^{-x^{2}}=(1-2x^{2})\e^{-x^{2}}$
\item $\D k'(x)=\frac{x\e^{x}-\e^{x}}{x^{2}}=\frac{(x-1)\e^{x}}{x^{2}}$
\item $\D r'(x)=2x\e^{-x}-x^{2}\e^{-x}=x(2-x)\e^{-x}$
\item $\D s'(x)=2x\e^{-x^{2}}-2x^{3}\e^{-x^{2}}=2x\left(1-x^{2}\right)\e^{-x^{2}}$
\item $\D t'(x)=-\e^{-x}\sin x+\e^{-x}\cos x=(\cos x-\sin x)\e^{-x}$
\item $\D u'(x)=\e^{\sin x}\cos x$
\item $\D v'(x)=\e^{x}\cos\left(\e^{x}\right)$ 
\end{enumerate}
}
