27v^2w/18v^3w eching

$$\frac { 27 v ^ { 2 } w } { 18 v ^ { 3 } w }$$

Baholash

$$\frac{3}{2v}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{27^{1}v^{2}w^{1}}{18^{1}v^{3}w^{1}}$$

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

$$\frac{27^{1}}{18^{1}}v^{2-3}w^{1-1}$$

2 dan 3 ni ayirish.

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}w^{1-1}$$

1 dan 1 ni ayirish.

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}w^{0}$$

Har qanday a raqami uchun (0 bundan mustasno) a^{0}=1.

$$\frac{27^{1}}{18^{1}}\times \frac{1}{v}$$

\frac{27}{18} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{2}\times \frac{1}{v}$$

v ga nisbatan hosilani topish

$$-\frac{3}{2v^{2}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{27w}{18w}v^{2-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{3}{2}\times \frac{1}{v})$$

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

$$-\frac{3}{2}v^{-1-1}$$

Arifmetik hisobni amalga oshirish.

$$-\frac{3}{2}v^{-2}$$