24x^7y^2/16x^3y^4 eching

$$\frac { 24 x ^ { 7 } y ^ { 2 } } { 16 x ^ { 3 } y ^ { 4 } }$$

Baholash

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

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{24^{1}x^{7}y^{2}}{16^{1}x^{3}y^{4}}$$

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

$$\frac{24^{1}}{16^{1}}x^{7-3}y^{2-4}$$

7 dan 3 ni ayirish.

$$\frac{24^{1}}{16^{1}}x^{4}y^{2-4}$$

2 dan 4 ni ayirish.

$$\frac{24^{1}}{16^{1}}x^{4}y^{-2}$$

\frac{24}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24y^{2}}{16y^{4}}x^{7-3})$$

Arifmetik hisobni amalga oshirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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