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. Birinchi hosila shundan iboratki,

\[\frac{{dy}}{{dz}} = - 5{{\bf{e}}^{ - 5z}} + 8\left( {\frac{{8{z^3}}}{{2{z^4}}}} \right) = - 5{{\bf{e}}^{ - 5z}} + 32{z^{ - 1}}\]

2-qadam

Ikkinchi hosila,

\[\frac{{{d^2}y}}{{d{z^2}}} = 25{{\bf{e}}^{ - 5z}} - 32{z^{ - 2}}\]

3-qadam

Uchinchi hosila,

\[\frac{{{d^3}y}}{{d{z^3}}} = - 125{{\bf{e}}^{ - 5z}} + 64{z^{ - 3}}\]

4-qadam

Ushbu muammoning to'rtinchi va oxirgi hosilasi:

\[\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{d^4}y}}{{d{z^4}}} = 625{{\bf{e}}^{ - 5z}} - 192{z^{ - 4}}}}\]