=x/15+x^2 eching

$$= \frac { x } { 15 + x ^ { 2 } }$$

x ga nisbatan hosilani topish

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

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.

$$\frac{\left(x^{2}+15\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+15)}{\left(x^{2}+15\right)^{2}}$$

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

$$\frac{\left(x^{2}+15\right)x^{1-1}-x^{1}\times 2x^{2-1}}{\left(x^{2}+15\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

1 dan 2 ni ayirish.

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

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

$$\frac{-x^{2}+15\times 1}{\left(x^{2}+15\right)^{2}}$$

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

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

Baholash

$$\frac{x}{x^{2}+15}$$