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

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

Solvi għal a (complex solution)

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

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

Immultiplika x u x biex tikseb x^{2}.

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

Immultiplika x u x biex tikseb x^{2}.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Naqqas 1 miż-żewġ naħat.

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

Naqqas x\times 2 miż-żewġ naħat.

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

Immultiplika -1 u 2 biex tikseb -2.

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

Ikkombina t-termini kollha li fihom a.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-2x^{2}-x.

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

Meta tiddividi b'-2x^{2}-x titneħħa l-multiplikazzjoni b'-2x^{2}-x.

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

Iddividi -1-2x b'-2x^{2}-x.

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

Solvi għal a

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

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

Immultiplika x u x biex tikseb x^{2}.

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

Immultiplika x u x biex tikseb x^{2}.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Naqqas 1 miż-żewġ naħat.

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

Naqqas x\times 2 miż-żewġ naħat.

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

Immultiplika -1 u 2 biex tikseb -2.

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

Ikkombina t-termini kollha li fihom a.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-2x^{2}-x.

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

Meta tiddividi b'-2x^{2}-x titneħħa l-multiplikazzjoni b'-2x^{2}-x.

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

Iddividi -1-2x b'-2x^{2}-x.

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

Solvi għal f (complex solution)

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

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

Solvi għal f

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

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