frac{2x^{3}y^3}{4x^3y^4*3x^3} eching

$$\frac { 2 x ^ { 3 } y ^ { 3 } } { 4 x ^ { 3 } y ^ { 4 } \cdot 3 x ^ { 3 } }$$

Baholash

$$\frac{1}{6yx^{3}}$$

Yechim qadamlari

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

$$\frac{2x^{3}y^{3}}{4x^{6}y^{4}\times 3}$$

Surat va maxrajdagi ikkala 2x^{3}y^{3} ni qisqartiring.

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

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{1}{6yx^{3}}$$

x ga nisbatan hosilani topish

$$-\frac{1}{2yx^{4}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{3}}{12x^{3}y^{4}}x^{3-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6yx^{3}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6yx^{3}})$$

Konstantaning hosilasi 0 ga teng.

$$0$$