Resolver (-2x)(-xy)^-1

$$( - 2 x ) ( - x y ) ^ { - 1 }$$

Calcular

$$\frac{2}{y}$$

Pasos da solución

Expande \left(\left(-x\right)y\right)^{-1}.

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

Expande \left(-x\right)^{-1}.

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

Calcula -1 á potencia de -1 e obtén -1.

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

Multiplica -2 e -1 para obter 2.

$$2xx^{-1}y^{-1}$$

Multiplica x e x^{-1} para obter 1.

$$2y^{-1}$$

Diferenciar w.r.t. y

$$-\frac{2}{y^{2}}$$

Pasos que usan a definición dunha derivada

Expande \left(\left(-x\right)y\right)^{-1}.

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

Expande \left(-x\right)^{-1}.

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

Calcula -1 á potencia de -1 e obtén -1.

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

Multiplica -2 e -1 para obter 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2xx^{-1}y^{-1})$$

Multiplica x e x^{-1} para obter 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{-1})$$

A derivada de ax^{n} é nax^{n-1}.

$$-2y^{-1-1}$$

Resta 1 de -1.

$$-2y^{-2}$$