f(t)=12t/3t^2+1 eching

$$f ( t ) = \frac { 12 t } { 3 t ^ { 2 } + 1 }$$

t ga nisbatan hosilani topish

$$\frac{12\left(1-3t^{2}\right)}{\left(3t^{2}+1\right)^{2}}$$

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.

$$\frac{\left(3t^{2}+1\right)\frac{\mathrm{d}}{\mathrm{d}t}(12t^{1})-12t^{1}\frac{\mathrm{d}}{\mathrm{d}t}(3t^{2}+1)}{\left(3t^{2}+1\right)^{2}}$$

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

$$\frac{\left(3t^{2}+1\right)\times 12t^{1-1}-12t^{1}\times 2\times 3t^{2-1}}{\left(3t^{2}+1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(3t^{2}+1\right)\times 12t^{0}-12t^{1}\times 6t^{1}}{\left(3t^{2}+1\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{3t^{2}\times 12t^{0}+12t^{0}-12t^{1}\times 6t^{1}}{\left(3t^{2}+1\right)^{2}}$$

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

$$\frac{3\times 12t^{2}+12t^{0}-12\times 6t^{1+1}}{\left(3t^{2}+1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{36t^{2}+12t^{0}-72t^{2}}{\left(3t^{2}+1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(36-72\right)t^{2}+12t^{0}}{\left(3t^{2}+1\right)^{2}}$$

36 dan 72 ni ayirish.

$$\frac{-36t^{2}+12t^{0}}{\left(3t^{2}+1\right)^{2}}$$

12 omili.

$$\frac{12\left(-3t^{2}+t^{0}\right)}{\left(3t^{2}+1\right)^{2}}$$

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

$$\frac{12\left(-3t^{2}+1\right)}{\left(3t^{2}+1\right)^{2}}$$

Baholash

$$\frac{12t}{3t^{2}+1}$$