derivative of Axe^{2x}

解答

\frac{d}{d x} (A x e^{2 x})

A (e^{2 x} + 2 e^{2 x} x)

求解步骤

\frac{d}{d x} (A x e^{2 x})

将常数提出:

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

= A \frac{d}{d x} (x e^{2 x})

使用微分乘法定则:

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

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

= A (\frac{d x}{d x} e^{2 x} + \frac{d}{d x} (e^{2 x}) x)

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

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

= A (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

化简

= A (e^{2 x} + 2 e^{2 x} x)

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