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 eching

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

Baholash

$$y$$

Qisqa yechim qadamlari

\frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} ni \frac{x}{\left(x+z\right)^{2}-y^{2}} ga bo'lish \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} ga k'paytirish \frac{x}{\left(x+z\right)^{2}-y^{2}} ga qaytarish.

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

\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} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x\left(x+y+z\right)\left(x+y-z\right) ni qisqartiring.

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

\frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-y-z ni qisqartiring.

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

x-y+z va x-y+z ni qisqartiring.

$$y$$

y ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

\frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} ni \frac{x}{\left(x+z\right)^{2}-y^{2}} ga bo'lish \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} ga k'paytirish \frac{x}{\left(x+z\right)^{2}-y^{2}} ga qaytarish.

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

\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} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x\left(x+y+z\right)\left(x+y-z\right) ni qisqartiring.

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

\frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-y-z ni qisqartiring.

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

x-y+z va x-y+z ni qisqartiring.

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

ax^{n} hosilasi – nax^{n-1}.

$$y^{1-1}$$

1 dan 1 ni ayirish.

$$y^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$1$$