(\partial)/(\partial x)((x^2-y^2)/(z^2))

解答

\frac{\partial}{\partial x} (\frac{x ^{2} - y ^{2}}{z ^{2}})

\frac{2 x}{z ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{x ^{2} - y ^{2}}{z ^{2}})

将

y, z

视为常数

将常数提出:

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

= \frac{1}{z ^{2}} \frac{\partial}{\partial x} (x^{2} - y^{2})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{z ^{2}} (\frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (y^{2}))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

= \frac{1}{z ^{2}} (2 x - 0)

化简

\frac{1}{z ^{2}} (2 x - 0) : \frac{2 x}{z ^{2}}

= \frac{2 x}{z ^{2}}

\frac{d}{d x} (x^{3} - \frac{3}{2} x^{2})

\int \frac{x ^{3} - x + 2}{x - 1} d x

l a pl a ce t r an s f or m e^{- 2 t} cos^{2} (t)

\frac{\partial}{\partial y} (24 y^{2} - 12 x)

\frac{\partial}{\partial x} (7 Y (x))