TeX Quellcode:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\left\{x\in\mathbb{R}\vert x\neq\pm\sqrt{\frac{\pi}{2}+k\pi} , k\in\mathbb{Z}\right\} \cr \cr f(x)&=&\dfrac{\sin(x)}{\cos(x^2)} \cr\cr \quad u(x) &=& \sin(x) & \Rightarrow & u'(x) &=& \cos(x) \cr \quad v(h(x)) &=& \cos(h(x)) & \Rightarrow & v'(x) &=& -\sin(h(x)) \cr \quad h(x) &=& x^2 & \Rightarrow & h'(x) &=& 2x \cr \cr f'(x) &=& \dfrac{\cos(x) \cdot \cos(x^2) - \sin(x) \cdot \left( -\sin(x^2) \right) \cdot 2x}{ \left( \cos(x^2) \right)^2 } \cr \cr &=&\dfrac{\cos(x) \cdot \cos(x^2)+2x \cdot \sin(x) \cdot \sin(x^2)}{\cos^2(x^2)}\end{array}