25x^2y^5/5x^4y^3 eching

$$\frac { 25 x ^ { 2 } y ^ { 5 } } { 5 x ^ { 4 } y ^ { 3 } }$$

Baholash

$$5\times \left(\frac{y}{x}\right)^{2}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{25^{1}x^{2}y^{5}}{5^{1}x^{4}y^{3}}$$

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

$$\frac{25^{1}}{5^{1}}x^{2-4}y^{5-3}$$

2 dan 4 ni ayirish.

$$\frac{25^{1}}{5^{1}}x^{-2}y^{5-3}$$

5 dan 3 ni ayirish.

$$\frac{25^{1}}{5^{1}}\times \frac{1}{x^{2}}y^{2}$$

25 ni 5 ga bo'lish.

$$5\times \frac{1}{x^{2}}y^{2}$$

x ga nisbatan hosilani topish

$$-\frac{10y^{2}}{x^{3}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25y^{5}}{5y^{3}}x^{2-4})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5y^{2}x^{-2})$$

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

$$-2\times 5y^{2}x^{-2-1}$$

Arifmetik hisobni amalga oshirish.

$$\left(-10y^{2}\right)x^{-3}$$