展开 1/81 (e^{9x}*9x-e^{9x})

解答

展开

\frac{1}{81} (e^{9 x} \cdot 9 x - e^{9 x})

\frac{e ^{9 x} x}{9} - \frac{1}{81} e^{9 x}

求解步骤

\frac{1}{81} (e^{9 x} \cdot 9 x - e^{9 x})

= \frac{1}{81} (9 e^{9 x} x - e^{9 x})

使用分配律:

a (b - c) = ab - a c

a = \frac{1}{81}, b = e^{9 x} \cdot 9 x, c = e^{9 x}

= \frac{1}{81} e^{9 x} \cdot 9 x - \frac{1}{81} e^{9 x}

= 9 \cdot \frac{1}{81} e^{9 x} x - \frac{1}{81} e^{9 x}

化简

9 \cdot \frac{1}{81} e^{9 x} x - \frac{1}{81} e^{9 x} : \frac{e ^{9 x} x}{9} - \frac{1}{81} e^{9 x}

= \frac{e ^{9 x} x}{9} - \frac{1}{81} e^{9 x}

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