d/dxx^2(2+x)/x^2-x eching

$$\frac { d } { d x } \frac { x ^ { 2 } ( 2 + x ) } { x ^ { 2 } - x }$$

Baholash

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{x^{2}\left(2+x\right)}{x^{2}-x} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+2x}{x-1})$$

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

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

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

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

Qisqartirish.

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

x^{1}-1 ni 2x^{1}+2x^{0} marotabaga ko'paytirish.

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

x^{2}+2x^{1} ni x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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

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

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

x ga nisbatan hosilani topish

$$\frac{6}{\left(x-1\right)^{3}}$$