TeX Quellcode:
\begin{array}{rcl} f'_{cc}(a,b,c) &=& 25\cdot\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}}+25c\cdot\left(-\dfrac{1}{2}\right)\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}-1}\cdot 50c \\\\&=& 25\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}}-625c^2\left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\ &=& \left[25\left(16a^2-b^2+25c^2\right)-625c^2\right] \left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\&=& \left[400a^2-25b^2+625c^2-625c^2\right] \left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\&=& \left[400a^2-25b^2\right] \left(16a^2-b^2+25c^2\right)^{-\frac{3}{2}} \\\\ &=& \dfrac{400a^2-25b^2}{\left(16a^2-b^2+25c^2\right)^{\frac{3}{2}}} \\\\&=& \dfrac{400a^2-25b^2}{\left(\sqrt{16a^2-b^2+25c^2}\right)^3}\end{array}