f^prime(x)=1/x-2ax+2-a eching

$$f ^ { \prime } ( x ) = \frac { 1 } { x } - 2 a x + 2 - a$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=-\frac{1}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xx=1-2axx+x\times 2-ax$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}=1-2axx+x\times 2-ax$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}=1-2ax^{2}+x\times 2-ax$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1-2ax^{2}+x\times 2-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$-2ax^{2}+x\times 2-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1$$

Ikkala tarafdan x\times 2 ni ayirish.

$$-2ax^{2}-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1-x\times 2$$

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$-2ax^{2}-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1-2x$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

$$\left(-2x^{2}-x\right)a=-2x-1$$

Ikki tarafini -2x^{2}-x ga bo‘ling.

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

-2x^{2}-x ga bo'lish -2x^{2}-x ga ko'paytirishni bekor qiladi.

$$a=\frac{-2x-1}{-2x^{2}-x}$$

-1-2x ni -2x^{2}-x ga bo'lish.

$$a=\frac{1}{x}$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq -\frac{1}{2}\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&x=-\frac{1}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xx=1-2axx+x\times 2-ax$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}=1-2axx+x\times 2-ax$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}=1-2ax^{2}+x\times 2-ax$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1-2ax^{2}+x\times 2-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}$$

Ikkala tarafdan 1 ni ayirish.

$$-2ax^{2}+x\times 2-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1$$

Ikkala tarafdan x\times 2 ni ayirish.

$$-2ax^{2}-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1-x\times 2$$

-2 hosil qilish uchun -1 va 2 ni ko'paytirish.

$$-2ax^{2}-ax=\frac{\mathrm{d}}{\mathrm{d}x}(f)x^{2}-1-2x$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

$$\left(-2x^{2}-x\right)a=-2x-1$$

Ikki tarafini -2x^{2}-x ga bo‘ling.

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

-2x^{2}-x ga bo'lish -2x^{2}-x ga ko'paytirishni bekor qiladi.

$$a=\frac{-2x-1}{-2x^{2}-x}$$

-1-2x ni -2x^{2}-x ga bo'lish.

$$a=\frac{1}{x}$$

f uchun yechish (complex solution)

$$f\in \mathrm{C}$$

$$x=-\frac{1}{2}\text{ or }\left(x=\frac{1}{a}\text{ and }a\neq 0\right)$$

f uchun yechish

$$f\in \mathrm{R}$$

$$x=-\frac{1}{2}\text{ or }\left(x=\frac{1}{a}\text{ and }a\neq 0\right)$$