(\partial)/(\partial x)(ue^{2x})

解答

\frac{\partial}{\partial x} (u (x) e^{2 x})

\frac{\partial}{\partial x} (u) e^{2 x} + e^{2 x} \cdot 2 u

求解步骤

\frac{\partial}{\partial x} (u e^{2 x})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = u, g = e^{2 x}

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

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

= \frac{\partial}{\partial x} (u) e^{2 x} + e^{2 x} \cdot 2 u

\int \frac{- 8}{( x - 2 ) ( x ^{2} + 4 )} d x

- 3 y^{^{'}} + 9 x^{2} = 0

\frac{\partial}{\partial x} (6 y^{2} x)

(x x)^{^{'}}

\frac{d y}{d t} + 7 y = e^{4 t}, y (0) = 10