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

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

Atrast a (complex solution)

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

Lineāra vienādojuma risināšanas darbības

Reiziniet vienādojuma abas puses ar x.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

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

Atņemiet 1 no abām pusēm.

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

Atņemiet x\times 2 no abām pusēm.

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

Reiziniet -1 un 2, lai iegūtu -2.

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

Savelciet visus locekļus, kuros ir a.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar -2x^{2}-x.

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

Dalīšana ar -2x^{2}-x atsauc reizināšanu ar -2x^{2}-x.

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

Daliet -1-2x ar -2x^{2}-x.

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

Atrast a

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

Lineāra vienādojuma risināšanas darbības

Reiziniet vienādojuma abas puses ar x.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Reiziniet x un x, lai iegūtu x^{2}.

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

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

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

Atņemiet 1 no abām pusēm.

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

Atņemiet x\times 2 no abām pusēm.

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

Reiziniet -1 un 2, lai iegūtu -2.

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

Savelciet visus locekļus, kuros ir a.

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

Vienādojums ir standarta formā.

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

Daliet abas puses ar -2x^{2}-x.

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

Dalīšana ar -2x^{2}-x atsauc reizināšanu ar -2x^{2}-x.

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

Daliet -1-2x ar -2x^{2}-x.

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

Atrast f (complex solution)

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

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

Atrast f

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

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