Resolver 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

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

Calcular

$$y$$

Pasos de solución curta

Divide \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} entre \frac{x}{\left(x+z\right)^{2}-y^{2}} mediante a multiplicación de \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} polo recíproco de \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Factoriza as expresións que aínda non o están en \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}.

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

Anula x\left(x+y+z\right)\left(x+y-z\right) no numerador e no denominador.

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

Factoriza as expresións que aínda non o están en \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Anula x-y-z no numerador e no denominador.

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

Anula x-y+z e x-y+z.

$$y$$

Diferenciar w.r.t. y

$$1$$

Pasos que usan a definición dunha derivada

Divide \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} entre \frac{x}{\left(x+z\right)^{2}-y^{2}} mediante a multiplicación de \frac{x^{2}+xy-xz}{\left(x+y\right)^{2}-z^{2}} polo recíproco de \frac{x}{\left(x+z\right)^{2}-y^{2}}.

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

Factoriza as expresións que aínda non o están en \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}.

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

Anula x\left(x+y+z\right)\left(x+y-z\right) no numerador e no denominador.

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

Factoriza as expresións que aínda non o están en \frac{xy-y^{2}-yz}{\left(x-y\right)^{2}-z^{2}}.

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

Anula x-y-z no numerador e no denominador.

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

Anula x-y+z e x-y+z.

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

A derivada de ax^{n} é nax^{n-1}.

$$y^{1-1}$$

Resta 1 de 1.

$$y^{0}$$

Para calquera termo t agás 0, t^{0}=1.

$$1$$