d/dxleft(x+1/x-3right) eching

$$\frac{d}{d x } \left( \frac{ x+1 }{ x-3 } \right)$$

Baholash

$$-\frac{4}{\left(x-3\right)^{2}}$$

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

1 dan 1 ni va -3 dan 1 ni ayiring.

$$\frac{-4x^{0}}{\left(x^{1}-3\right)^{2}}$$

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

$$\frac{-4x^{0}}{\left(x-3\right)^{2}}$$

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

$$\frac{-4}{\left(x-3\right)^{2}}$$

x ga nisbatan hosilani topish

$$\frac{8}{\left(x-3\right)^{3}}$$