TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D}&=&\left\{t \in \mathbb{R}\; |\; t\neq \frac{\pi}{2}+2 k \pi \text{ und } t\neq \frac{3\pi}{2}+2 k \pi , k \in \mathbb{Z} \right\} \cr \cr y(t) &=& \dfrac{\sin{\left(t \right)}}{\cos{\left(t \right)}} \cr \cr \quad u(t) &=& \sin{\left(t \right)} & \Rightarrow & u'(t) &=&\cos{\left(t \right)}\cr \quad v(t) &=&\cos{\left(t \right)} & \Rightarrow & v'(t) &=& - \sin{\left(t \right)} \cr \cr y'(t) &=& \dfrac{\cos{\left(t \right)}\cdot \cos{\left(t \right)}-\sin{\left(t \right)}\cdot \left(- \sin{\left(t \right)}\right)}{\left(\cos{\left(t \right)}\right)^2} \cr \cr &=& \dfrac{\cos^{2}{\left(t \right)}+ \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} \cr \cr &=& \dfrac{1}{\cos^{2}{\left(t \right)}} \end{array}