x/2y2/3xy^2 eching

$$\frac { x } { 2 y } \frac { 2 } { 3 x y ^ { 2 } }$$

Baholash

$$\frac{1}{3y^{3}}$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x}{2y} ni \frac{2}{3xy^{2}} ga ko‘paytiring.

$$\frac{x\times 2}{2y\times 3xy^{2}}$$

Surat va maxrajdagi ikkala 2x ni qisqartiring.

$$\frac{1}{3yy^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$\frac{1}{3y^{3}}$$

y ga nisbatan hosilani topish

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

Zanjirli qoidadan foydalanish qadamalari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x}{2y} ni \frac{2}{3xy^{2}} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x\times 2}{2y\times 3xy^{2}})$$

Surat va maxrajdagi ikkala 2x ni qisqartiring.

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

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

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.

$$-\left(3y^{3}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}y}(3y^{3})$$

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

$$-\left(3y^{3}\right)^{-2}\times 3\times 3y^{3-1}$$

Qisqartirish.

$$-9y^{2}\times \left(3y^{3}\right)^{-2}$$