3x/x^2+x-7 eching

$$\frac { 3 x } { x ^ { 2 } + x - 7 }$$

x ga nisbatan hosilani topish

$$\frac{3\left(-x^{2}-7\right)}{\left(x^{2}+x-7\right)^{2}}$$

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.

$$\frac{\left(x^{2}+x^{1}-7\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1}-7)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

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

$$\frac{\left(x^{2}+x^{1}-7\right)\times 3x^{1-1}-3x^{1}\left(2x^{2-1}+x^{1-1}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}+x^{1}-7\right)\times 3x^{0}-3x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

x^{2}+x^{1}-7 ni 3x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 3x^{0}+x^{1}\times 3x^{0}-7\times 3x^{0}-3x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

3x^{1} ni 2x^{1}+x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 3x^{0}+x^{1}\times 3x^{0}-7\times 3x^{0}-\left(3x^{1}\times 2x^{1}+3x^{1}x^{0}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

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

$$\frac{3x^{2}+3x^{1}-7\times 3x^{0}-\left(3\times 2x^{1+1}+3x^{1}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

Qisqartirish.

$$\frac{3x^{2}+3x^{1}-21x^{0}-\left(6x^{2}+3x^{1}\right)}{\left(x^{2}+x^{1}-7\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-3x^{2}-21x^{0}}{\left(x^{2}+x^{1}-7\right)^{2}}$$

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

$$\frac{-3x^{2}-21x^{0}}{\left(x^{2}+x-7\right)^{2}}$$

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

$$\frac{-3x^{2}-21}{\left(x^{2}+x-7\right)^{2}}$$

Baholash

$$\frac{3x}{x^{2}+x-7}$$