f(x)=5x/7-x eching

$$f ( x ) = \frac { 5 x } { 7 - x }$$

x ga nisbatan hosilani topish

$$\frac{35}{\left(x-7\right)^{2}}$$

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.

$$\frac{\left(-x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})-5x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+7)}{\left(-x^{1}+7\right)^{2}}$$

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

$$\frac{\left(-x^{1}+7\right)\times 5x^{1-1}-5x^{1}\left(-1\right)x^{1-1}}{\left(-x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(-x^{1}+7\right)\times 5x^{0}-5x^{1}\left(-1\right)x^{0}}{\left(-x^{1}+7\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{-x^{1}\times 5x^{0}+7\times 5x^{0}-5x^{1}\left(-1\right)x^{0}}{\left(-x^{1}+7\right)^{2}}$$

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

$$\frac{-5x^{1}+7\times 5x^{0}-5\left(-1\right)x^{1}}{\left(-x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-5x^{1}+35x^{0}-\left(-5x^{1}\right)}{\left(-x^{1}+7\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-5-\left(-5\right)\right)x^{1}+35x^{0}}{\left(-x^{1}+7\right)^{2}}$$

-5 dan -5 ni ayirish.

$$\frac{35x^{0}}{\left(-x^{1}+7\right)^{2}}$$

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

$$\frac{35x^{0}}{\left(-x+7\right)^{2}}$$

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

$$\frac{35\times 1}{\left(-x+7\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{35}{\left(-x+7\right)^{2}}$$

Baholash

$$\frac{5x}{7-x}$$