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人気のある微分積分 >

derivative of ax^2e^x

解

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

解

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

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

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

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

グラフ

人気の例

(\partial)/(\partial y)(3x^2-2y^2)

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

limit as x approaches infinity of x/((ln(x))^x)

x \to \infty lim (\frac{x}{( ln ( x ) ) ^{x}})

(\partial)/(\partial x)(n^2x*(1-x)^n)

\frac{\partial}{\partial x} (n^{2} x \cdot (1 - x)^{n})

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\int \frac{1}{( x ^{2} + 2 x + 2 ) ^{2}} d x

\frac{d y}{d t} + 2 y = 1