8y/12y-18y^2 eching

$$\frac { 8 y } { 12 y - 18 y ^ { 2 } }$$

Baholash

$$\frac{4}{3\left(2-3y\right)}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{8y}{6y\left(-3y+2\right)}$$

Surat va maxrajdagi ikkala 2y ni qisqartiring.

$$\frac{4}{3\left(-3y+2\right)}$$

Ifodani kengaytiring.

$$\frac{4}{-9y+6}$$

y ga nisbatan hosilani topish

$$\frac{4}{\left(2-3y\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\left(12y^{1}-18y^{2}\right)\frac{\mathrm{d}}{\mathrm{d}y}(8y^{1})-8y^{1}\frac{\mathrm{d}}{\mathrm{d}y}(12y^{1}-18y^{2})}{\left(12y^{1}-18y^{2}\right)^{2}}$$

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

$$\frac{\left(12y^{1}-18y^{2}\right)\times 8y^{1-1}-8y^{1}\left(12y^{1-1}+2\left(-18\right)y^{2-1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(12y^{1}-18y^{2}\right)\times 8y^{0}-8y^{1}\left(12y^{0}-36y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

12y^{1}-18y^{2} ni 8y^{0} marotabaga ko'paytirish.

$$\frac{12y^{1}\times 8y^{0}-18y^{2}\times 8y^{0}-8y^{1}\left(12y^{0}-36y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

8y^{1} ni 12y^{0}-36y^{1} marotabaga ko'paytirish.

$$\frac{12y^{1}\times 8y^{0}-18y^{2}\times 8y^{0}-\left(8y^{1}\times 12y^{0}+8y^{1}\left(-36\right)y^{1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

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

$$\frac{12\times 8y^{1}-18\times 8y^{2}-\left(8\times 12y^{1}+8\left(-36\right)y^{1+1}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

Qisqartirish.

$$\frac{96y^{1}-144y^{2}-\left(96y^{1}-288y^{2}\right)}{\left(12y^{1}-18y^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{144y^{2}}{\left(12y^{1}-18y^{2}\right)^{2}}$$

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

$$\frac{144y^{2}}{\left(12y-18y^{2}\right)^{2}}$$