[(y^3)]^5/[(y^6)]^4 eching

$$\frac { [ ( y ^ { 3 } ) ] ^ { 5 } } { [ ( y ^ { 6 } ) ] ^ { 4 } }$$

Baholash

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

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 5 ni ko‘paytirib, 15 ni oling.

$$\frac{y^{15}}{\left(y^{6}\right)^{4}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 4 ni ko‘paytirib, 24 ni oling.

$$\frac{y^{15}}{y^{24}}$$

y^{24} ni y^{15}y^{9} sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{15} ni qisqartiring.

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

y ga nisbatan hosilani topish

$$-\frac{9}{y^{10}}$$

Zanjirli qoidadan foydalanish qadamalari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 5 ni ko‘paytirib, 15 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{15}}{\left(y^{6}\right)^{4}})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 4 ni ko‘paytirib, 24 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{15}}{y^{24}})$$

y^{24} ni y^{15}y^{9} sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{15} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{y^{9}})$$

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$-\left(y^{9}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}y}(y^{9})$$

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

$$-\left(y^{9}\right)^{-2}\times 9y^{9-1}$$

Qisqartirish.

$$-9y^{8}\left(y^{9}\right)^{-2}$$