maclaurin x^2e^{2x}

Lösung

maclaurin

x^{2} e^{2 x}

x^{2} + 2 x^{3} + 2 x^{4} + \frac{4}{3} x^{5} + \frac{2}{3} x^{6} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{160}{5 !} x^{5} + \frac{480}{6 !} x^{6} + \dots

Fasse zusammen

= x^{2} + 2 x^{3} + 2 x^{4} + \frac{4}{3} x^{5} + \frac{2}{3} x^{6} + \dots

\int (4 x) d x

\int \frac{z}{x - 3} d x

\int x^{2} + 5 x d x

\frac{\partial}{\partial x} (5 x^{4} + x^{3} y + x y + y^{4})

\frac{\partial}{\partial y} (4 x y^{2})