Bu muammo to'rtta hosila olishdan boshqa narsa emas, shuning uchun har bir qadam biz to'rtinchi darajaga yetguncha har bir keyingi hosilani ko'rsatadi. Funktsiyani tezda qayta yozgandan so'ng, farqlashda yordam berish uchun birinchi hosila:

\[f\left( x \right) = 4\,{x^{\frac{3}{5}}} - \frac{1}{8}{x^{ - 2}} - {x^{\frac{1}{2}}}\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}f'\left( x \right) = \frac{{12}}{5}\,{x^{ - \,\,\frac{2}{5}}} + \frac{1}{4}{x^{ - 3}} - \frac{1}{2}{x^{ - \,\,\frac{1}{2}}}\]

2-qadam

Ikkinchi hosila,

\[f''\left( x \right) = - \frac{{24}}{{25}}\,{x^{ - \,\,\frac{7}{5}}} - \frac{3}{4}{x^{ - 4}} + \frac{1}{4}{x^{ - \,\,\frac{3}{2}}}\]

3-qadam

Uchinchi hosila,

\[f'''\left( x \right) = \frac{{168}}{{125}}\,{x^{ - \,\,\frac{{12}}{5}}} + 3{x^{ - 5}} - \frac{3}{8}{x^{ - \,\,\frac{5}{2}}}\]

4-qadam

Ushbu muammoning to'rtinchi va oxirgi hosilasi:

\[\require{bbox} \bbox[2pt,border:1px solid black]{{{f^{\left( 4 \right)}}\left( x \right) = - \frac{{2016}}{{625}}\,{x^{ - \,\,\frac{{17}}{5}}} - 15{x^{ - 6}} + \frac{{15}}{{16}}{x^{ - \,\,\frac{7}{2}}}}}\]