Ushbu muammo uchun har bir atama Zanjir qoidasining alohida qo'llanilishini talab qiladi va birinchi muddatda ildiz bilan ishlashda qavslar bilan ehtiyot bo'lishingizga ishonch hosil qiling.

Demak, hosila,

\[S\left( w \right) = {\left( {7w} \right)^{\frac{1}{2}}} + {{\bf{e}}^{ - w}}\hspace{0.25in}\,\, \Rightarrow \hspace{0.25in}S'\left( w \right) = \frac{1}{2}\left( 7 \right){\left( {7w} \right)^{ - \,\,\,\frac{1}{2}}} - {{\bf{e}}^{ - w}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{7}{2}{{\left( {7w} \right)}^{ - \,\,\,\frac{1}{2}}} - {{\bf{e}}^{ - w}}}}\]