6x^1/5/3x^1/7 eching

$$\frac { 6 x ^ { 1 / 5 } } { 3 x ^ { 1 / 7 } }$$

Baholash

$$2x^{\frac{2}{35}}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(6\sqrt[5]{x}\right)^{1}\times \frac{1}{3\sqrt[7]{x}}$$

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

$$6^{1}\left(\sqrt[5]{x}\right)^{1}\times \frac{1}{3}\times \frac{1}{\sqrt[7]{x}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$6^{1}\times \frac{1}{3}\left(\sqrt[5]{x}\right)^{1}\times \frac{1}{\sqrt[7]{x}}$$

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

$$6^{1}\times \frac{1}{3}\sqrt[5]{x}x^{\frac{1}{7}\left(-1\right)}$$

\frac{1}{7} ni -1 marotabaga ko'paytirish.

$$6^{1}\times \frac{1}{3}\sqrt[5]{x}x^{-\frac{1}{7}}$$

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

$$6^{1}\times \frac{1}{3}x^{\frac{1}{5}-\frac{1}{7}}$$

\frac{1}{5} va -\frac{1}{7} belgilarini qo'shish.

$$6^{1}\times \frac{1}{3}x^{\frac{2}{35}}$$

6 ni 1 daraja ko'rsatgichiga oshirish.

$$6\times \frac{1}{3}x^{\frac{2}{35}}$$

6 ni \frac{1}{3} marotabaga ko'paytirish.

$$2x^{\frac{2}{35}}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{6^{1}\sqrt[5]{x}}{3^{1}\sqrt[7]{x}}$$

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

$$\frac{6^{1}x^{\frac{1}{5}-\frac{1}{7}}}{3^{1}}$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{7} ni \frac{1}{5} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$\frac{6^{1}x^{\frac{2}{35}}}{3^{1}}$$

6 ni 3 ga bo'lish.

$$2x^{\frac{2}{35}}$$

x ga nisbatan hosilani topish

$$\frac{4}{35x^{\frac{33}{35}}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{3}x^{\frac{1}{5}-\frac{1}{7}})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{2}{35}})$$

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

$$\frac{2}{35}\times 2x^{\frac{2}{35}-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{4}{35}x^{-\frac{33}{35}}$$