derivative y=x^3e^{4x}

解答

导数

y = x^{3} e^{4 x}

3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

求解步骤

\frac{d}{d x} (x^{3} e^{4 x})

使用微分乘法定则:

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

f = x^{3}, g = e^{4 x}

= \frac{d}{d x} (x^{3}) e^{4 x} + \frac{d}{d x} (e^{4 x}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 3 x^{2} e^{4 x} + e^{4 x} \cdot 4 x^{3}

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