d/dt(t^2-1/2t) eching

$$\frac { d } { d t } ( \frac { t ^ { 2 } - 1 } { 2 t } )$$

Baholash

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

4 dan 2 ni ayirish.

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

2 omili.

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

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

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

2 ni 2 daraja ko'rsatgichiga oshirish.

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

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

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

t ga nisbatan hosilani topish

$$-\frac{1}{t^{3}}$$