What is maclaurin x^3e^{2x} ?

The answer to maclaurin x^3e^{2x} is x^3+2x^4+2x^5+4/3 x^6+2/3 x^7+\ldots

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maclaurin x^3e^{2x}

maclaurin

x^{3} e^{2 x}

x^{3} + 2 x^{4} + 2 x^{5} + \frac{4}{3} x^{6} + \frac{2}{3} x^{7} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \frac{240}{5 !} x^{5} + \frac{960}{6 !} x^{6} + \frac{3360}{7 !} x^{7} + \dots

Refine

= x^{3} + 2 x^{4} + 2 x^{5} + \frac{4}{3} x^{6} + \frac{2}{3} x^{7} + \dots

n = 0 \sum \infty \frac{x ^{n}}{3 \cdot n}

y = \frac{3}{x}

\frac{d}{d t} (\frac{1}{2 t ^{2} + 1})

\frac{\partial}{\partial x} (8 y - 2)

y^{^{'}} = 3 x^{2} e^{- y}

What is maclaurin x^3e^{2x} ?
The answer to maclaurin x^3e^{2x} is x^3+2x^4+2x^5+4/3 x^6+2/3 x^7+\ldots