frac{10p^{4}q^{3}*2p^2q^3}{5p^8q^3} eching

$$\frac { 10 p ^ { 4 } q ^ { 3 } \times 2 p ^ { 2 } q ^ { 3 } } { 5 p ^ { 8 } q ^ { 3 } }$$

Baholash

$$\frac{4q^{3}}{p^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 2 ni qo‘shib, 6 ni oling.

$$\frac{10p^{6}q^{3}\times 2q^{3}}{5p^{8}q^{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 3 ni qo‘shib, 6 ni oling.

$$\frac{10p^{6}q^{6}\times 2}{5p^{8}q^{3}}$$

Surat va maxrajdagi ikkala 5q^{3}p^{6} ni qisqartiring.

$$\frac{2\times 2q^{3}}{p^{2}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{4q^{3}}{p^{2}}$$

p ga nisbatan hosilani topish

$$-8\times \left(\frac{q}{p}\right)^{3}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{20p^{2}q^{6}}{5q^{3}}p^{4-8})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}p}(4p^{2}q^{3}p^{-4})$$

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

$$-4\times 4p^{2}q^{3}p^{-4-1}$$

Arifmetik hisobni amalga oshirish.

$$\left(-16p^{2}q^{3}\right)p^{-5}$$