derivative 11x^2e^x

解答

导数

11 x^{2} e^{x}

11 (2 x e^{x} + e^{x} x^{2})

求解步骤

\frac{d}{d x} (11 x^{2} e^{x})

将常数提出:

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

= 11 \frac{d}{d x} (x^{2} e^{x})

使用微分乘法定则:

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

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

= 11 (\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}

= 11 (2 x e^{x} + e^{x} x^{2})

n = 0 \sum \infty \frac{e ^{n}}{( n ! )}

\int (e^{4 x}) d x

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