d/dxleft(4x/4-x^2right) eching

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

Baholash

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{-4x^{2}+16x^{0}-\left(-8x^{2}\right)}{\left(-x^{2}+4\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-4-\left(-8\right)\right)x^{2}+16x^{0}}{\left(-x^{2}+4\right)^{2}}$$

-4 dan -8 ni ayirish.

$$\frac{4x^{2}+16x^{0}}{\left(-x^{2}+4\right)^{2}}$$

4 omili.

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

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

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

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

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

x ga nisbatan hosilani topish

$$-\frac{8x\left(x^{2}+12\right)}{\left(x^{2}-4\right)^{3}}$$