TeX source:
\begin{array}{rcl} f'_b(a,b,c) &=& \dfrac{1}{2}\left(16a^2-b^2+25c^2\right)^{\frac{1}{2}-1} \cdot (-2b) \\\\&=& -b\left(16a^2-b^2+25c^2\right)^{-\frac{1}{2}} \\\\&=& -\dfrac{b}{\sqrt{16a^2-b^2+25c^2}}\end{array}