f(1)=14x^2/x^4+49 eching

$$f ( 1 ) = \frac { 14 x ^ { 2 } } { x ^ { 4 } + 49 }$$

x ga nisbatan hosilani topish

$$\frac{28x\left(49-x^{4}\right)}{\left(x^{4}+49\right)^{2}}$$

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.

$$\frac{\left(x^{4}+49\right)\frac{\mathrm{d}}{\mathrm{d}x}(14x^{2})-14x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}+49)}{\left(x^{4}+49\right)^{2}}$$

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

$$\frac{\left(x^{4}+49\right)\times 2\times 14x^{2-1}-14x^{2}\times 4x^{4-1}}{\left(x^{4}+49\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{4}+49\right)\times 28x^{1}-14x^{2}\times 4x^{3}}{\left(x^{4}+49\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{4}\times 28x^{1}+49\times 28x^{1}-14x^{2}\times 4x^{3}}{\left(x^{4}+49\right)^{2}}$$

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

$$\frac{28x^{4+1}+49\times 28x^{1}-14\times 4x^{2+3}}{\left(x^{4}+49\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{28x^{5}+1372x^{1}-56x^{5}}{\left(x^{4}+49\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(28-56\right)x^{5}+1372x^{1}}{\left(x^{4}+49\right)^{2}}$$

28 dan 56 ni ayirish.

$$\frac{-28x^{5}+1372x^{1}}{\left(x^{4}+49\right)^{2}}$$

28x omili.

$$\frac{28x\left(-x^{4}+49x^{0}\right)}{\left(x^{4}+49\right)^{2}}$$

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

$$\frac{28x\left(-x^{4}+49\times 1\right)}{\left(x^{4}+49\right)^{2}}$$

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

$$\frac{28x\left(-x^{4}+49\right)}{\left(x^{4}+49\right)^{2}}$$

Baholash

$$\frac{14x^{2}}{x^{4}+49}$$