3xy/6x-3xy eching

$$\frac { 3 x y } { 6 x - 3 x y }$$

Baholash

$$\frac{y}{2-y}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{3xy}{3x\left(-y+2\right)}$$

Surat va maxrajdagi ikkala 3x ni qisqartiring.

$$\frac{y}{-y+2}$$

y ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{3xy}{6x-3xy} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3xy}{3x\left(-y+2\right)})$$

Surat va maxrajdagi ikkala 3x ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{-y+2})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(-y^{1}+2\right)\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})-y^{1}\frac{\mathrm{d}}{\mathrm{d}y}(-y^{1}+2)}{\left(-y^{1}+2\right)^{2}}$$

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

$$\frac{\left(-y^{1}+2\right)y^{1-1}-y^{1}\left(-1\right)y^{1-1}}{\left(-y^{1}+2\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(-y^{1}+2\right)y^{0}-y^{1}\left(-1\right)y^{0}}{\left(-y^{1}+2\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{-y^{1}y^{0}+2y^{0}-y^{1}\left(-1\right)y^{0}}{\left(-y^{1}+2\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{-y^{1}+2y^{0}-\left(-y^{1}\right)}{\left(-y^{1}+2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-1-\left(-1\right)\right)y^{1}+2y^{0}}{\left(-y^{1}+2\right)^{2}}$$

-1 dan -1 ni ayirish.

$$\frac{2y^{0}}{\left(-y^{1}+2\right)^{2}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{2y^{0}}{\left(-y+2\right)^{2}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

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

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{2}{\left(-y+2\right)^{2}}$$