Lahenda frac{x^{2}+xy-xz}{(x+y)^{2}-z^{2}}divx/(x+z)^{2-y^2}*xy-y^2-yz/(x-y)^2-z^2

$$\frac { x ^ { 2 } + x y - x z } { ( x + y ) ^ { 2 } - z ^ { 2 } } \div \frac { x } { ( x + z ) ^ { 2 } - y ^ { 2 } } \cdot \frac { x y - y ^ { 2 } - y z } { ( x - y ) ^ { 2 } - z ^ { 2 } }$$

Arvuta

$$y$$

Lühike lahenduskäik

Jagage \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} väärtusega \frac{x}{\left(x+z\right)^{2}-y^{2}}, korrutades \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} väärtuse \frac{x}{\left(x+z\right)^{2}-y^{2}} pöördväärtusega.

$$\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}$$

Kui avaldised pole tehtes \frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x} veel teguriteks lahutatud, tehke seda.

$$\frac{x\left(x+y+z\right)\left(x+y-z\right)\left(x-y+z\right)}{x\left(x+y+z\right)\left(x+y-z\right)}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}$$

Taandage x\left(x+y+z\right)\left(x+y-z\right) nii lugejas kui ka nimetajas.

$$\left(x-y+z\right)\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}$$

Kui avaldised pole tehtes \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} veel teguriteks lahutatud, tehke seda.

$$\left(x-y+z\right)\times \frac{y\left(x-y-z\right)}{\left(x-y+z\right)\left(x-y-z\right)}$$

Taandage x-y-z nii lugejas kui ka nimetajas.

$$\left(x-y+z\right)\times \frac{y}{x-y+z}$$

Taandage x-y+z ja x-y+z.

$$y$$

Diferentseeri y-i järgi

$$1$$

Juhised tuletise definitsiooni kasutamisel

Jagage \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} väärtusega \frac{x}{\left(x+z\right)^{2}-y^{2}}, korrutades \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} väärtuse \frac{x}{\left(x+z\right)^{2}-y^{2}} pöördväärtusega.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

Kui avaldised pole tehtes \frac{\left(x^{2}+xy-xz\right)\left(\left(x+z\right)^{2}-y^{2}\right)}{\left(\left(x+y\right)^{2}-z^{2}\right)x} veel teguriteks lahutatud, tehke seda.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x\left(x+y+z\right)\left(x+y-z\right)\left(x-y+z\right)}{x\left(x+y+z\right)\left(x+y-z\right)}\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

Taandage x\left(x+y+z\right)\left(x+y-z\right) nii lugejas kui ka nimetajas.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}})$$

Kui avaldised pole tehtes \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} veel teguriteks lahutatud, tehke seda.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{y\left(x-y-z\right)}{\left(x-y+z\right)\left(x-y-z\right)})$$

Taandage x-y-z nii lugejas kui ka nimetajas.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(x-y+z\right)\times \frac{y}{x-y+z})$$

Taandage x-y+z ja x-y+z.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y)$$

ax^{n} tuletis on nax^{n-1}.

$$y^{1-1}$$

Lahutage 1 väärtusest 1.

$$y^{0}$$

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

$$1$$