麦克劳林 e^x+e^{2x}

解答

麦克劳林

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

2 + 3 x + \frac{5}{2} x^{2} + \frac{3}{2} x^{3} + \frac{17}{24} x^{4} + \dots

求解步骤

应用麦克劳林公式

= 2 + \frac{\frac{d}{d x} ( e ^{x} + e ^{2 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x} + e ^{2 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x} + e ^{2 x} ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 2 + \frac{3}{1 !} x + \frac{5}{2 !} x^{2} + \frac{9}{3 !} x^{3} + \frac{17}{4 !} x^{4} + \dots

整理后得

= 2 + 3 x + \frac{5}{2} x^{2} + \frac{3}{2} x^{3} + \frac{17}{24} x^{4} + \dots

\int x - 1 d x

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\frac{\partial}{\partial y} (cos (x y) y)

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