5x^-2/5x^2 eching

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

Baholash

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

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(5x^{-2}\right)^{1}\times \frac{1}{5x^{2}}$$

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

$$5^{1}\left(x^{-2}\right)^{1}\times \frac{1}{5}\times \frac{1}{x^{2}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$5^{1}\times \frac{1}{5}\left(x^{-2}\right)^{1}\times \frac{1}{x^{2}}$$

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

$$5^{1}\times \frac{1}{5}x^{-2}x^{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

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

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

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

-2 va -2 belgilarini qo'shish.

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

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

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

1 va -1 belgilarini qo'shish.

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

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

$$1x^{-4}$$

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

$$x^{-4}$$

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{5}x^{-2-2})$$

Arifmetik hisobni amalga oshirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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