9x^2/3x^2-3x eching

$$\frac{ 9 { x }^{ 2 } }{ 3 { x }^{ 2 } -3x }$$

Baholash

$$\frac{3x}{x-1}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{9x^{2}}{3x\left(x-1\right)}$$

Surat va maxrajdagi ikkala 3x ni qisqartiring.

$$\frac{3x}{x-1}$$

x ga nisbatan hosilani topish

$$-\frac{3}{\left(x-1\right)^{2}}$$

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.

$$\frac{\left(3x^{2}-3x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2})-9x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-3x^{1})}{\left(3x^{2}-3x^{1}\right)^{2}}$$

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

$$\frac{\left(3x^{2}-3x^{1}\right)\times 2\times 9x^{2-1}-9x^{2}\left(2\times 3x^{2-1}-3x^{1-1}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(3x^{2}-3x^{1}\right)\times 18x^{1}-9x^{2}\left(6x^{1}-3x^{0}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

3x^{2}-3x^{1} ni 18x^{1} marotabaga ko'paytirish.

$$\frac{3x^{2}\times 18x^{1}-3x^{1}\times 18x^{1}-9x^{2}\left(6x^{1}-3x^{0}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

9x^{2} ni 6x^{1}-3x^{0} marotabaga ko'paytirish.

$$\frac{3x^{2}\times 18x^{1}-3x^{1}\times 18x^{1}-\left(9x^{2}\times 6x^{1}+9x^{2}\left(-3\right)x^{0}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

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

$$\frac{3\times 18x^{2+1}-3\times 18x^{1+1}-\left(9\times 6x^{2+1}+9\left(-3\right)x^{2}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{54x^{3}-54x^{2}-\left(54x^{3}-27x^{2}\right)}{\left(3x^{2}-3x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-27x^{2}}{\left(3x^{2}-3x^{1}\right)^{2}}$$

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

$$\frac{-27x^{2}}{\left(3x^{2}-3x\right)^{2}}$$