40x^4/12x^2 eching

$$\frac { 40 x ^ { 4 } } { 12 x ^ { 2 } }$$

Baholash

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

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(40x^{4}\right)^{1}\times \frac{1}{12x^{2}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$40^{1}\left(x^{4}\right)^{1}\times \frac{1}{12}\times \frac{1}{x^{2}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$40^{1}\times \frac{1}{12}\left(x^{4}\right)^{1}\times \frac{1}{x^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$40^{1}\times \frac{1}{12}x^{4}x^{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$40^{1}\times \frac{1}{12}x^{4}x^{-2}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$40^{1}\times \frac{1}{12}x^{4-2}$$

4 va -2 belgilarini qo'shish.

$$40^{1}\times \frac{1}{12}x^{2}$$

40 ni 1 daraja ko'rsatgichiga oshirish.

$$40\times \frac{1}{12}x^{2}$$

40 ni \frac{1}{12} marotabaga ko'paytirish.

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

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{40^{1}x^{4}}{12^{1}x^{2}}$$

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

$$\frac{40^{1}x^{4-2}}{12^{1}}$$

4 dan 2 ni ayirish.

$$\frac{40^{1}x^{2}}{12^{1}}$$

\frac{40}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x ga nisbatan hosilani topish

$$\frac{20x}{3}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{40}{12}x^{4-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{3}x^{2})$$

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

$$2\times \frac{10}{3}x^{2-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{20}{3}x^{1}$$

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

$$\frac{20}{3}x$$