d/dx(2/x-3/x^2)= eching

$$\frac { d } { d x } ( \frac { 2 } { x } - \frac { 3 } { x ^ { 2 } } ) =$$

Baholash

$$\frac{2\left(3-x\right)}{x^{3}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x^{2} ning eng kichik umumiy karralisi x^{2}. \frac{2}{x} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{x^{2}}-\frac{3}{x^{2}})$$

\frac{2x}{x^{2}} va \frac{3}{x^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-3}{x^{2}})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

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

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

$$\frac{x^{2}\times 2x^{1-1}-\left(2x^{1}-3\right)\times 2x^{2-1}}{\left(x^{2}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{x^{2}\times 2x^{0}-\left(2x^{1}-3\right)\times 2x^{1}}{\left(x^{2}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 2x^{0}-\left(2x^{1}\times 2x^{1}-3\times 2x^{1}\right)}{\left(x^{2}\right)^{2}}$$

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{2}-\left(4x^{2}-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{2x^{2}-4x^{2}-\left(-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-4\right)x^{2}-\left(-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

2 dan 4 ni ayirish.

$$\frac{-2x^{2}-\left(-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

2x omili.

$$\frac{2x\left(-x^{1}-\left(-3x^{0}\right)\right)}{\left(x^{2}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$\frac{2x\left(-x^{1}-\left(-3x^{0}\right)\right)}{x^{2\times 2}}$$

2 ni 2 marotabaga ko'paytirish.

$$\frac{2x\left(-x^{1}-\left(-3x^{0}\right)\right)}{x^{4}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{2\left(-x^{1}-\left(-3x^{0}\right)\right)}{x^{4-1}}$$

4 dan 1 ni ayirish.

$$\frac{2\left(-x^{1}-\left(-3x^{0}\right)\right)}{x^{3}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{2\left(-x-\left(-3x^{0}\right)\right)}{x^{3}}$$

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

$$\frac{2\left(-x-\left(-3\right)\right)}{x^{3}}$$

x ga nisbatan hosilani topish

$$\frac{2\left(2x-9\right)}{x^{4}}$$