x^199/x^200+100 eching

$$\frac { x ^ { 199 } } { x ^ { 200 } + 100 }$$

x ga nisbatan hosilani topish

$$\frac{x^{198}\left(19900-x^{200}\right)}{\left(x^{200}+100\right)^{2}}$$

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.

$$\frac{\left(x^{200}+100\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{199})-x^{199}\frac{\mathrm{d}}{\mathrm{d}x}(x^{200}+100)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{\left(x^{200}+100\right)\times 199x^{199-1}-x^{199}\times 200x^{200-1}}{\left(x^{200}+100\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{200}+100\right)\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{200}\times 199x^{198}+100\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{199x^{200+198}+100\times 199x^{198}-200x^{199+199}}{\left(x^{200}+100\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{199x^{398}+19900x^{198}-200x^{398}}{\left(x^{200}+100\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(199-200\right)x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

199 dan 200 ni ayirish.

$$\frac{-x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

x^{198} omili.

$$\frac{x^{198}\left(-x^{200}+19900x^{0}\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\times 1\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\right)}{\left(x^{200}+100\right)^{2}}$$

Baholash

$$\frac{x^{199}}{x^{200}+100}$$