derivative of Cxe^x

解答

\frac{d}{d x} (C x e^{x})

C (e^{x} + e^{x} x)

求解步骤

\frac{d}{d x} (C x e^{x})

将

C

视为常数

将常数提出:

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

= C \frac{d}{d x} (x e^{x})

使用微分乘法定则:

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

f = x, g = e^{x}

= C (\frac{d x}{d x} e^{x} + \frac{d}{d x} (e^{x}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x}) = e^{x}

= C (1 \cdot e^{x} + e^{x} x)

化简

= C (e^{x} + e^{x} x)

\int_{0}^{1} 6

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

\frac{\partial}{\partial x} (\frac{3 x - 2 y}{x ^{2} + 3 y})

\int \frac{cos ( x )}{sin ^{2} ( x ) - 36} d x

y^{^{''}} + 2 y^{^{'}} + 122 y = 0