81x^2/6x eching

$$\frac{ 81 { x }^{ 2 } }{ 6x }$$

Baholash

$$\frac{27x}{2}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{81^{1}x^{2}}{6^{1}x^{1}}$$

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

$$\frac{81^{1}x^{2-1}}{6^{1}}$$

2 dan 1 ni ayirish.

$$\frac{81^{1}x^{1}}{6^{1}}$$

\frac{81}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{27}{2}x^{1}$$

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

$$\frac{27}{2}x$$

x ga nisbatan hosilani topish

$$\frac{27}{2} = 13\frac{1}{2} = 13,5$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{81}{6}x^{2-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{27}{2}x^{1})$$

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

$$\frac{27}{2}x^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{27}{2}x^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{27}{2}\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{27}{2}$$