frac{2x^{4}*(x^2y^4)^-1}{2yx^2} eching

$$\frac { 2 x ^ { 4 } \cdot ( x ^ { 2 } y ^ { 4 } ) ^ { - 1 } } { 2 y x ^ { 2 } }$$

Baholash

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

Yechim qadamlari

Surat va maxrajdagi ikkala 2x^{2} ni qisqartiring.

$$\frac{\frac{1}{x^{2}y^{4}}x^{2}}{y}$$

\frac{1}{x^{2}y^{4}}x^{2} ni yagona kasrga aylantiring.

$$\frac{\frac{x^{2}}{x^{2}y^{4}}}{y}$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

$$\frac{\frac{1}{y^{4}}}{y}$$

\frac{\frac{1}{y^{4}}}{y} ni yagona kasrga aylantiring.

$$\frac{1}{y^{4}y}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 1 ni qo‘shib, 5 ni oling.

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

y ga nisbatan hosilani topish

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

Zanjirli qoidadan foydalanish qadamalari

Surat va maxrajdagi ikkala 2x^{2} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{1}{x^{2}y^{4}}x^{2}}{y})$$

\frac{1}{x^{2}y^{4}}x^{2} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{x^{2}}{x^{2}y^{4}}}{y})$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\frac{1}{y^{4}}}{y})$$

\frac{\frac{1}{y^{4}}}{y} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{y^{4}y})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 1 ni qo‘shib, 5 ni oling.

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

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.

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