Ushbu muammo uchun ildizni kasr ko'rsatkichiga aylantirgandan so'ng, tashqi funktsiya (umid qilamanki) aniq \(\frac{1}{3}\) ko'rsatkichi bo'ladi, ichki funksiya esa kuchga ko'tariladigan ko'phad (yoki ildiz ichidagi ko'phad - bu haqda qanday o'ylashni xohlayotganingizga qarab). Demak, hosila,

\[y = {\left( {1 - 8z} \right)^{\frac{1}{3}}}\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\,\,\,\,\,\,\,\,\,\,\frac{{dy}}{{dz}} = \frac{1}{3}{\left( {1 - 8z} \right)^{ - \,\,\frac{2}{3}}}\left( { - 8} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{8}{3}{{\left( {1 - 8z} \right)}^{ - \,\,\frac{2}{3}}}}}\]