frac{y^frac{2{5}}(y^3)^frac{1{2}}}{y^frac{1{10}}} eching

$$\frac { y ^ { \frac { 2 } { 5 } } ( y ^ { 3 } ) ^ { \frac { 1 } { 2 } } } { y ^ { \frac { 1 } { 10 } } }$$

y ga nisbatan hosilani topish

$$\frac{9y^{\frac{4}{5}}}{5}$$

Derivativ ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va \frac{1}{2} ni ko‘paytirib, \frac{3}{2} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{\frac{2}{5}}y^{\frac{3}{2}}}{y^{\frac{1}{10}}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{2}{5} va \frac{3}{2} ni qo‘shib, \frac{19}{10} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{\frac{19}{10}}}{y^{\frac{1}{10}}})$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. \frac{19}{10} dan \frac{1}{10} ni ayirib, \frac{9}{5} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{9}{5}})$$

ax^{n} hosilasi – nax^{n-1}.

$$\frac{9}{5}y^{\frac{9}{5}-1}$$

\frac{9}{5} dan 1 ni ayirish.

$$\frac{9}{5}y^{\frac{4}{5}}$$

Baholash

$$y^{\frac{9}{5}}$$