f(x)=x/x+5 eching

$$f ( x ) = \frac { x } { x + 5 }$$

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

O'xshash hadlarni birlashtirish.

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

1 dan 1 ni ayirish.

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

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

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

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

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

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

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

Baholash

$$\frac{x}{x+5}$$