maclaurin e^{3x}-e^{2x}

Lösung

maclaurin

e^{3 x} - e^{2 x}

x + \frac{5}{2} x^{2} + \frac{19}{6} x^{3} + \frac{65}{24} x^{4} + \frac{211}{120} x^{5} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{5}{2 !} x^{2} + \frac{19}{3 !} x^{3} + \frac{65}{4 !} x^{4} + \frac{211}{5 !} x^{5} + \dots

Fasse zusammen

= x + \frac{5}{2} x^{2} + \frac{19}{6} x^{3} + \frac{65}{24} x^{4} + \frac{211}{120} x^{5} + \dots

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