\ANG{
Berechne jeweils die Ableitung:
\begin{enumerate}
  \item $f_1:x\mapsto y = f_1\left(x\right)=x+e^{x^2}$
  \item $f_2:x\mapsto y = f_2\left(x\right)=e^{-x} + \sin x$
  \item $f_3:x\mapsto y = f_3\left(x\right)=5\,e^{\sqrt{\sin x}}$
  \item $f_4:x\mapsto y = f_4\left(x\right)=e^{\sin\left(x^2\right)}$
  \item $f_5:x\mapsto y = f_5\left(x\right)=x\,e^{\sqrt{x}}$
  \item $f_6:x\mapsto y = f_6\left(x\right)=x\,e^{x\,\sin x}$
  \item $f_7:x\mapsto y = f_7\left(x\right)=2^{\ln x}$
  \item $f_8:x\mapsto y = f_8\left(x\right)=x^{\sqrt{x}}$
\end{enumerate}
}
\LSG{
$1 + 2\,x\cdot e^{x^2}$,
$-e^{-x}+\cos x$,
$5\cdot\frac{\cos x\cdot e^{\sqrt{\sin x}}}{2\cdot\sqrt{\sin x}}$,
$2\,x\cdot\cos\left(x^2\right)\cdot e^{\sin\left(x^2\right)}$,

$e^{\sqrt{x}}+\frac{\sqrt{x}\cdot e^{\sqrt{x}}}{2}$,
$e^{x\,\sin x} + x\,e^{x\,\sin x}\cdot\left(x\,\cos x + \sin x\right)$,
$\frac{\ln 2 \cdot 2^{\ln x}}{x}$,
$\frac{x}{\sqrt{x}}\left(1+\frac{\ln x}{2}\right)$.
}
