d/dz(z+3/2z-4) eching

$$\frac { d } { d z } ( \frac{z+3}{2z-4} )$$

Baholash

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

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.

$$\frac{\left(2z^{1}-4\right)\frac{\mathrm{d}}{\mathrm{d}z}(z^{1}+3)-\left(z^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}z}(2z^{1}-4)}{\left(2z^{1}-4\right)^{2}}$$

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

$$\frac{\left(2z^{1}-4\right)z^{1-1}-\left(z^{1}+3\right)\times 2z^{1-1}}{\left(2z^{1}-4\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{2z^{1}-4z^{0}-\left(2z^{1}+6z^{0}\right)}{\left(2z^{1}-4\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{2z^{1}-4z^{0}-2z^{1}-6z^{0}}{\left(2z^{1}-4\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-2\right)z^{1}+\left(-4-6\right)z^{0}}{\left(2z^{1}-4\right)^{2}}$$

2 dan 2 ni va -4 dan 6 ni ayiring.

$$\frac{-10z^{0}}{\left(2z^{1}-4\right)^{2}}$$

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

$$\frac{-10z^{0}}{\left(2z-4\right)^{2}}$$

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

$$\frac{-10}{\left(2z-4\right)^{2}}$$

z ga nisbatan hosilani topish

$$\frac{5}{\left(z-2\right)^{3}}$$