frac{r^{9}s^{2}t^{0}}{r^{-84}s^{3}t^0*r^12s^4t^5} eching

$$\frac { r ^ { 9 } s ^ { 2 } t ^ { 0 } } { r ^ { - 84 } s ^ { 3 } t ^ { 0 } \cdot r ^ { 12 } s ^ { 4 } t ^ { 5 } }$$

Baholash

$$\frac{r^{81}}{\left(st\right)^{5}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -84 va 12 ni qo‘shib, -72 ni oling.

$$\frac{r^{9}s^{2}t^{0}}{r^{-72}s^{3}t^{0}s^{4}t^{5}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 4 ni qo‘shib, 7 ni oling.

$$\frac{r^{9}s^{2}t^{0}}{r^{-72}s^{7}t^{0}t^{5}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 0 va 5 ni qo‘shib, 5 ni oling.

$$\frac{r^{9}s^{2}t^{0}}{r^{-72}s^{7}t^{5}}$$

Surat va maxrajdagi ikkala s^{2} ni qisqartiring.

$$\frac{t^{0}r^{9}}{r^{-72}s^{5}t^{5}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{t^{0}r^{81}}{s^{5}t^{5}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{r^{81}}{s^{5}t^{5}}$$

r ga nisbatan hosilani topish

$$\frac{81r^{80}}{\left(st\right)^{5}}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{t^{0}s^{2}}{t^{0}s^{3}s^{4}t^{5}r^{12}}r^{9-\left(-84\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{r^{12}\left(st\right)^{5}}r^{93})$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$93\times \frac{1}{r^{12}\left(st\right)^{5}}r^{93-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{93}{r^{12}\left(st\right)^{5}}r^{92}$$