TeX Quellcode:

\begin{array}{lclcrcl}\quad\mathbb{D} &=& \mathbb{R} \\\\f(z) &=& -\dfrac{3}{10}\sqrt{1+\cos\left(z^2\right)} \\\\&=& -\dfrac{3}{10}\left(1+\cos\left(z^2\right)\right)^{\frac{1}{2}} \\\\\quad g(h(k(z))) &=& -\dfrac{3}{10}\left(h(k(z))\right)^{\frac{1}{2}} & \Rightarrow & g'(h(k(z))) &=& -\dfrac{3}{20}\left(h(k(z))\right)^{-\frac{1}{2}} \\\\\quad h(k(z)) &=& 1+\cos\left(k(z)\right) & \Rightarrow & h'(k(z)) &=& -\sin\left(k(z)\right) \\\\\quad k(z) &=& z^2 & \Rightarrow & k'(z) &=& 2z \\\\f'(z) &=& -\dfrac{3}{20}\left(1+\cos\left(z^2\right)\right)^{-\frac{1}{2}}\cdot \left(-\sin\left(z^2\right)\right)\cdot 2z \\\\&=& \dfrac{3z\cdot \sin\left(z^2\right)}{10\left(1+\cos\left(z^2\right)\right)^{\frac{1}{2}}} \\\\&=& \dfrac{3z\cdot \sin\left(z^2\right)}{10\sqrt{1+\cos(z^2)}}\end{array}