4x^1/2/8x^1/3 eching

$$\frac { 4 x ^ { 1 / 2 } } { 8 x ^ { 1 / 3 } }$$

Baholash

$$\frac{\sqrt[6]{x}}{2}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{4^{1}\sqrt{x}}{8^{1}\sqrt[3]{x}}$$

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

$$\frac{4^{1}x^{\frac{1}{2}-\frac{1}{3}}}{8^{1}}$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{3} ni \frac{1}{2} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$\frac{4^{1}\sqrt[6]{x}}{8^{1}}$$

\frac{4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}\sqrt[6]{x}$$

x ga nisbatan hosilani topish

$$\frac{1}{12x^{\frac{5}{6}}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{8}x^{\frac{1}{2}-\frac{1}{3}})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\sqrt[6]{x})$$

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

$$\frac{1}{6}\times \frac{1}{2}x^{\frac{1}{6}-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{1}{12}x^{-\frac{5}{6}}$$