3x^-2y^-3/6x^-4y^-1 eching

$$\frac { 3 x ^ { - 2 } y ^ { - 3 } } { 6 x ^ { - 4 } y ^ { - 1 } }$$

Baholash

$$\frac{\left(\frac{x}{y}\right)^{2}}{2}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{y^{-3}x^{-2}}{2x^{-4}\times \frac{1}{y}}$$

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

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

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

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

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{y^{3}\times \frac{6}{y}}x^{-2-\left(-4\right)})$$

Arifmetik hisobni amalga oshirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

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

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