maclaurin x^2e^{4x}

Lösung

maclaurin

x^{2} e^{4 x}

x^{2} + 4 x^{3} + 8 x^{4} + \frac{32}{3} x^{5} + \frac{32}{3} x^{6} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( x ^{2} e ^{4 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{2} e ^{4 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{2} e ^{4 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{192}{4 !} x^{4} + \frac{1280}{5 !} x^{5} + \frac{7680}{6 !} x^{6} + \dots

Fasse zusammen

= x^{2} + 4 x^{3} + 8 x^{4} + \frac{32}{3} x^{5} + \frac{32}{3} x^{6} + \dots

\frac{d y}{d x} = e^{- ka \cdot x}, y (0) = 0

\int \frac{x ^{2} - x + 12}{x ^{3} + 6 x} d x

\frac{\partial}{\partial x} (e^{3 x} sin (cy))

n = 0 \sum \infty \frac{3 ^{n}}{2 ^{n}}

d er i v a t i v e f (x) = \frac{1}{2 - 3 x}