x^-1/4x^4 eching

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

Baholash

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

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

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

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

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

Ko'paytirishning kommutativ xususiyatidan foydalanish.

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

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

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

4 ni -1 marotabaga ko'paytirish.

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

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

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

-1 va -4 belgilarini qo'shish.

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

4 ni -1 daraja ko'rsatgichiga oshirish.

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

x ga nisbatan hosilani topish

$$-\frac{5}{4x^{6}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{-1-4})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{-5})$$

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

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

Arifmetik hisobni amalga oshirish.

$$-\frac{5}{4}x^{-6}$$