f(t)=2t/1+2t^2 eching

$$f ( t ) = \frac { 2 t } { 1 + 2 t ^ { 2 } }$$

t ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{4t^{2}+2t^{0}-8t^{2}}{\left(2t^{2}+1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(4-8\right)t^{2}+2t^{0}}{\left(2t^{2}+1\right)^{2}}$$

4 dan 8 ni ayirish.

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

2 omili.

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

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

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

Baholash

$$\frac{2t}{2t^{2}+1}$$