x^frac{1{3}}divx^frac{2{3}} eching

$$x ^ { \frac { 1 } { 3 } } \div x ^ { \frac { 2 } { 3 } }$$

Baholash

$$\frac{1}{\sqrt[3]{x}}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{\sqrt[3]{x}}{x^{\frac{2}{3}}}$$

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

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

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

$$x^{-\frac{1}{3}}$$

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

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

Arifmetik hisobni amalga oshirish.

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

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

$$-\frac{1}{3}x^{-\frac{1}{3}-1}$$

Arifmetik hisobni amalga oshirish.

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