x^2/x^2+x-12 eching

$$\frac { x ^ { 2 } } { x ^ { 2 } + x - 12 }$$

x ga nisbatan hosilani topish

$$\frac{x\left(x-24\right)}{\left(\left(x-3\right)\left(x+4\right)\right)^{2}}$$

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.

$$\frac{\left(x^{2}+x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})-x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1}-12)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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

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

Qisqartirish.

$$\frac{\left(x^{2}+x^{1}-12\right)\times 2x^{1}-x^{2}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

x^{2}+x^{1}-12 ni 2x^{1} marotabaga ko'paytirish.

$$\frac{x^{2}\times 2x^{1}+x^{1}\times 2x^{1}-12\times 2x^{1}-x^{2}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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

$$\frac{x^{2}\times 2x^{1}+x^{1}\times 2x^{1}-12\times 2x^{1}-\left(x^{2}\times 2x^{1}+x^{2}x^{0}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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

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

Qisqartirish.

$$\frac{2x^{3}+2x^{2}-24x^{1}-\left(2x^{3}+x^{2}\right)}{\left(x^{2}+x^{1}-12\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{x^{2}-24x^{1}}{\left(x^{2}+x^{1}-12\right)^{2}}$$

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

$$\frac{x^{2}-24x}{\left(x^{2}+x-12\right)^{2}}$$

Baholash

$$\frac{x^{2}}{x^{2}+x-12}$$