f(x)=3x/x-5 eching

$$f ( x ) = \frac { 3 x } { x - 5 }$$

x ga nisbatan hosilani topish

$$-\frac{15}{\left(x-5\right)^{2}}$$

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.

$$\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{\left(x^{1}-5\right)\times 3x^{1-1}-3x^{1}x^{1-1}}{\left(x^{1}-5\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}-5\right)\times 3x^{0}-3x^{1}x^{0}}{\left(x^{1}-5\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 3x^{0}-5\times 3x^{0}-3x^{1}x^{0}}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{3x^{1}-5\times 3x^{0}-3x^{1}}{\left(x^{1}-5\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{1}-15x^{0}-3x^{1}}{\left(x^{1}-5\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-3\right)x^{1}-15x^{0}}{\left(x^{1}-5\right)^{2}}$$

3 dan 3 ni ayirish.

$$\frac{-15x^{0}}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{-15x^{0}}{\left(x-5\right)^{2}}$$

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

$$\frac{-15}{\left(x-5\right)^{2}}$$

Baholash

$$\frac{3x}{x-5}$$