4x^2/4x^7 eching

$$\frac { 4 x ^ { 2 } } { 4 x ^ { 7 } }$$

Baholash

$$\frac{1}{x^{5}}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(4x^{2}\right)^{1}\times \frac{1}{4x^{7}}$$

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

$$4^{1}\left(x^{2}\right)^{1}\times \frac{1}{4}\times \frac{1}{x^{7}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$4^{1}\times \frac{1}{4}\left(x^{2}\right)^{1}\times \frac{1}{x^{7}}$$

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

$$4^{1}\times \frac{1}{4}x^{2}x^{7\left(-1\right)}$$

7 ni -1 marotabaga ko'paytirish.

$$4^{1}\times \frac{1}{4}x^{2}x^{-7}$$

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

$$4^{1}\times \frac{1}{4}x^{2-7}$$

2 va -7 belgilarini qo'shish.

$$4^{1}\times \frac{1}{4}x^{-5}$$

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

$$4^{1-1}x^{-5}$$

1 va -1 belgilarini qo'shish.

$$4^{0}x^{-5}$$

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

$$1x^{-5}$$

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

$$x^{-5}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{4^{1}x^{2}}{4^{1}x^{7}}$$

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

$$4^{1-1}x^{2-7}$$

1 dan 1 ni ayirish.

$$4^{0}x^{2-7}$$

Har qanday a raqami uchun (0 bundan mustasno) a^{0}=1.

$$x^{2-7}$$

2 dan 7 ni ayirish.

$$x^{-5}$$

x ga nisbatan hosilani topish

$$-\frac{5}{x^{6}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{4}x^{2-7})$$

Arifmetik hisobni amalga oshirish.

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

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

$$-5x^{-5-1}$$

Arifmetik hisobni amalga oshirish.

$$-5x^{-6}$$