TeX Quellcode:

\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R}^+ \\\\f(a) &=& -14\sqrt[4]{a}\cdot \log_4(a) \\\\\quad u(a) &=& -14\sqrt[4]{a} = -14a^{\frac{1}{4}} &\Rightarrow & u'(a) &=& -14\cdot\frac{1}{4}a^{-\frac{3}{4}} = -\dfrac{7}{2}a^{-\frac{3}{4}} \\\quad v(a) &=& \log_4(a) &\Rightarrow & v'(a) &=& \dfrac{1}{a\ln(4)} \\\\f'(a) &=& -\dfrac{7}{2}a^{-\frac{3}{4}}\cdot \log_4(a)-14\sqrt[4]{a}\cdot \dfrac{1}{a\ln(4)} \\&=& -\dfrac{7}{2}a^{-\frac{3}{4}}\cdot\log_4(a)-14a^{-\frac{3}{4}}\cdot\dfrac{1}{\ln(4)} \\&=& -\dfrac{7}{\sqrt[4]{a^3}}\left(\dfrac{\log_4(a)}{2}+\dfrac{2}{\ln(4)}\right)\end{array}