(\partial)/(\partial x)((w)(u(w,v,x)^2+e^{2v}))

解答

\frac{\partial}{\partial x} ((w) (u (w, v, x) (w, v, x)^{2} + e^{2 v}))

w ((\frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)) + 0)

求解步骤

\frac{\partial}{\partial x} ((w) (u (w, v, x) (w, v, x)^{2} + e^{2 v}))

将

w, v

视为常数

将常数提出:

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

= w \frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2} + e^{2 v})

使用微分加减法定则:

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

= w (\frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2}) + \frac{\partial}{\partial x} (e^{2 v}))

\frac{\partial}{\partial x} (u (w, v, x) (w, v, x)^{2}) = \frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)

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

= w ((\frac{\partial}{\partial x} (u (w, v, x)) (w, v, x)^{2} + 2 (w, v, x) (w, v, 1) u (w, v, x)) + 0)

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e x p an d \frac{x ^{n + 1}}{( n + 1 ) n !}

e x p an d \frac{( 18 n - 7 ) ^{2}}{441}

e x p an d \frac{e ^{- 5 s} ( 2 s + 3 )}{s ( s ^{2} + 2 s + 5 )}

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