TeX Quellcode:
\begin{array}{rcl} f'_{aa}(a,b,c) &=& 16\cdot\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}}+16a\cdot\left(-\dfrac{1}{2}\right)\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}-1}\cdot 32a \\\\&=& 16\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}}-256a^2\left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\ &=& \left[16\left(16a^2-b^2+25c^2\right)-256a^2\right] \left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\&=& \left[256a^2-16b^2+400c^2-256a^2\right]\left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\&=& \left[-16b^2+400c^2\right]\left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\&=& \dfrac{-16b^2+400c^2}{\left(16a^2-b^2+25c^2\right)^{\frac{3}{2}}} \\\\&=& \dfrac{-16b^2+400c^2}{\left(\sqrt{16a^2-b^2+25c^2}\right)^3}\end{array}