TeX source:
\begin{array}{rcl}f'_{bb}(a,b,c) &=& \dfrac{3\pi}{2}\cdot 2a^2b^{2-1}c+2\cdot 51\pi ab^{2-1}+62c^2\\\\&=& 3\pi a^2bc+102\pi ab+62c^2\end{array}