9x^2y^4/6xy^7 eching

$$\frac { 9 x ^ { 2 } y ^ { 4 } } { 6 x y ^ { 7 } }$$

Baholash

$$\frac{3x}{2y^{3}}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{9^{1}x^{2}y^{4}}{6^{1}x^{1}y^{7}}$$

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

$$\frac{9^{1}}{6^{1}}x^{2-1}y^{4-7}$$

2 dan 1 ni ayirish.

$$\frac{9^{1}}{6^{1}}x^{1}y^{4-7}$$

4 dan 7 ni ayirish.

$$\frac{9^{1}}{6^{1}}xy^{-3}$$

\frac{9}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{2}x\times \frac{1}{y^{3}}$$

x ga nisbatan hosilani topish

$$\frac{3}{2y^{3}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9y^{4}}{6y^{7}}x^{2-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2y^{3}}x^{1})$$

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

$$\frac{3}{2y^{3}}x^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3}{2y^{3}}x^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{3}{2y^{3}}\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{3}{2y^{3}}$$