展开 (10x^2+2x)e^{10x}

解答

展开

(10 x^{2} + 2 x) e^{10 x}

10 e^{10 x} x^{2} + 2 e^{10 x} x

求解步骤

(10 x^{2} + 2 x) e^{10 x}

= e^{10 x} (10 x^{2} + 2 x)

使用分配律:

a (b + c) = ab + a c

a = e^{10 x}, b = 10 x^{2}, c = 2 x

= e^{10 x} \cdot 10 x^{2} + e^{10 x} \cdot 2 x

= 10 e^{10 x} x^{2} + 2 e^{10 x} x

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