frac{u^frac{2{3}}}{u^frac{3{5}}} eching

$$\frac { u ^ { \frac { 2 } { 3 } } } { u ^ { \frac { 3 } { 5 } } }$$

Baholash

$$\sqrt[15]{u}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{u^{\frac{2}{3}}}{u^{\frac{3}{5}}}$$

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

$$u^{\frac{2}{3}-\frac{3}{5}}$$

Umumiy maxrajni topib va suratlarni ayirib \frac{3}{5} ni \frac{2}{3} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$\sqrt[15]{u}$$

u ga nisbatan hosilani topish

$$\frac{1}{15u^{\frac{14}{15}}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{1}{1}u^{\frac{2}{3}-\frac{3}{5}})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt[15]{u})$$

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

$$\frac{1}{15}u^{\frac{1}{15}-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{1}{15}u^{-\frac{14}{15}}$$