Réitigh f^prime(x)=1/x-2ax+2-a

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

Réitigh do a. (complex solution)

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi x.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Bain 1 ón dá thaobh.

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

Bain x\times 2 ón dá thaobh.

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

Méadaigh -1 agus 2 chun -2 a fháil.

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

Comhcheangail na téarmaí ar fad ina bhfuil a.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -2x^{2}-x.

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

Má roinntear é faoi -2x^{2}-x cuirtear an iolrúchán faoi -2x^{2}-x ar ceal.

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

Roinn -1-2x faoi -2x^{2}-x.

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

Réitigh do a.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi x.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Bain 1 ón dá thaobh.

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

Bain x\times 2 ón dá thaobh.

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

Méadaigh -1 agus 2 chun -2 a fháil.

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

Comhcheangail na téarmaí ar fad ina bhfuil a.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -2x^{2}-x.

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

Má roinntear é faoi -2x^{2}-x cuirtear an iolrúchán faoi -2x^{2}-x ar ceal.

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

Roinn -1-2x faoi -2x^{2}-x.

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

Réitigh do f. (complex solution)

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

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

Réitigh do f.

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

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