Lahenda 1/x^2-2x+5dx

$$\frac { 1 } { x ^ { 2 } - 2 x + 5 } d x$$

Arvuta

$$\frac{dx}{x^{2}-2x+5}$$

Lahenduse etapid

Avaldage \frac{1}{x^{2}-2x+5}d ühe murdarvuna.

$$\frac{d}{x^{2}-2x+5}x$$

Avaldage \frac{d}{x^{2}-2x+5}x ühe murdarvuna.

$$\frac{dx}{x^{2}-2x+5}$$

Diferentseeri x-i järgi

$$\frac{d\left(5-x^{2}\right)}{\left(x^{2}-2x+5\right)^{2}}$$

Juhised jagatise tuletisereegli kasutamisel

Avaldage \frac{1}{x^{2}-2x+5}d ühe murdarvuna.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{d}{x^{2}-2x+5}x)$$

Avaldage \frac{d}{x^{2}-2x+5}x ühe murdarvuna.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{dx}{x^{2}-2x+5})$$

Iga kahe diferentseeruva funktsiooni korral on kahe funktsiooni jagatise tuletis nimetaja korda lugeja tuletis miinus lugeja korda nimetaja tuletis, mis on seejärel jagatud nimetaja ruuduga.

$$\frac{\left(x^{2}-2x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(dx^{1})-dx^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}+5)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Polünoomi tuletis on polünoomi liikmete tuletiste summa. Mis tahes vabaliikme tuletis on 0. ax^{n} tuletis on nax^{n-1}.

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{1-1}-dx^{1}\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Lihtsustage.

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Korrutage omavahel x^{2}-2x^{1}+5 ja dx^{0}.

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Korrutage omavahel dx^{1} ja 2x^{1}-2x^{0}.

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-\left(dx^{1}\times 2x^{1}+dx^{1}\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Sama alusega astmete korrutamiseks liitke nende astendajad.

$$\frac{dx^{2}-2dx^{1}+5dx^{0}-\left(d\times 2x^{1+1}+d\left(-2\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Lihtsustage.

$$\frac{dx^{2}+\left(-2d\right)x^{1}+5dx^{0}-\left(2dx^{2}+\left(-2d\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Kombineerige sarnased liikmed.

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Mis tahes liikme t korral on t^{1}=t.

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x+5\right)^{2}}$$

Iga Termini t peale 0, t^{0}=1.

$$\frac{\left(-d\right)x^{2}+5d\times 1}{\left(x^{2}-2x+5\right)^{2}}$$

t t\times 1=t ja 1t=t.

$$\frac{\left(-d\right)x^{2}+5d}{\left(x^{2}-2x+5\right)^{2}}$$