(\partial)/(\partial y)(x(e^y+e^{-y}))

解答

\frac{\partial}{\partial y} (x (e^{y} + e^{- y}))

x (e^{y} - e^{- y})

求解步骤

\frac{\partial}{\partial y} (x (e^{y} + e^{- y}))

将

x

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (e^{y} + e^{- y})

使用微分加减法定则:

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

= x (\frac{\partial}{\partial y} (e^{y}) + \frac{\partial}{\partial y} (e^{- y}))

\frac{\partial}{\partial y} (e^{y}) = e^{y}

\frac{\partial}{\partial y} (e^{- y}) = - e^{- y}

= x (e^{y} - e^{- y})

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