y^2y^0/y^7 eching

$$\frac{ { y }^{ 2 } { y }^{ 0 } }{ { y }^{ 7 } }$$

Baholash

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

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 0 ni qo‘shib, 2 ni oling.

$$\frac{y^{2}}{y^{7}}$$

y^{7} ni y^{2}y^{5} sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{2} ni qisqartiring.

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

y ga nisbatan hosilani topish

$$-\frac{5}{y^{6}}$$

Zanjirli qoidadan foydalanish qadamalari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 0 ni qo‘shib, 2 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{2}}{y^{7}})$$

y^{7} ni y^{2}y^{5} sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{2} ni qisqartiring.

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

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.

$$-\left(y^{5}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}y}(y^{5})$$

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

$$-\left(y^{5}\right)^{-2}\times 5y^{5-1}$$

Qisqartirish.

$$-5y^{4}\left(y^{5}\right)^{-2}$$