(\partial)/(\partial x)((x^αy^β)/(y^{1-α)x^{1-β}})

解答

\frac{\partial}{\partial x} (\frac{x ^{α} y ^{β}}{y ^{1 - α} x ^{1 - β}})

x^{α + β - 2} y^{β - 1 + α} (α - 1 + β)

求解步骤

\frac{\partial}{\partial x} (\frac{x ^{α} y ^{β}}{y ^{1 - α} x ^{1 - β}})

化简

\frac{x ^{α} y ^{β}}{y ^{1 - α} x ^{1 - β}} : x^{α - 1 + β} y^{β - 1 + α}

= \frac{\partial}{\partial x} (x^{α - 1 + β} y^{β - 1 + α})

将

α, β, y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y^{β - 1 + α} \frac{\partial}{\partial x} (x^{α - 1 + β})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y^{β - 1 + α} (α - 1 + β) x^{α - 1 + β - 1}

化简

= x^{α + β - 2} y^{β - 1 + α} (α - 1 + β)

\frac{\partial}{\partial x} ((1 + \frac{2}{y}) sin (x))

\frac{d}{d x} (2 x z (x))

x \to 1 lim (- 6 + 4 x^{2})

a re a 2 x - 5 y = 0, y = 0, x = 5

\int 4 + 25 x^{2} d x