40xy^5/16x^2y^3 eching

$$\frac { 40 x y ^ { 5 } } { 16 x ^ { 2 } y ^ { 3 } }$$

Baholash

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

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{40^{1}x^{1}y^{5}}{16^{1}x^{2}y^{3}}$$

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

$$\frac{40^{1}}{16^{1}}x^{1-2}y^{5-3}$$

1 dan 2 ni ayirish.

$$\frac{40^{1}}{16^{1}}\times \frac{1}{x}y^{5-3}$$

5 dan 3 ni ayirish.

$$\frac{40^{1}}{16^{1}}\times \frac{1}{x}y^{2}$$

\frac{40}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{40y^{5}}{16y^{3}}x^{1-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{2}}{2}\times \frac{1}{x})$$

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

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

Arifmetik hisobni amalga oshirish.

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