5x/x-3 eching

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

5 dan 5 ni ayirish.

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

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

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

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

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

Baholash

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