5p^3q^2/25pq= eching

$$\frac { 5 p ^ { 3 } q ^ { 2 } } { 25 p q } =$$

Baholash

$$\frac{qp^{2}}{5}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{5^{1}p^{3}q^{2}}{25^{1}p^{1}q^{1}}$$

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

$$\frac{5^{1}}{25^{1}}p^{3-1}q^{2-1}$$

3 dan 1 ni ayirish.

$$\frac{5^{1}}{25^{1}}p^{2}q^{2-1}$$

2 dan 1 ni ayirish.

$$\frac{5^{1}}{25^{1}}p^{2}q^{1}$$

\frac{5}{25} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{5}p^{2}q$$

p ga nisbatan hosilani topish

$$\frac{2pq}{5}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5q^{2}}{25q}p^{3-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{q}{5}p^{2})$$

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

$$2\times \frac{q}{5}p^{2-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2q}{5}p^{1}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{2q}{5}p$$