What is maclaurin 2xe^{x^2} ?

The answer to maclaurin 2xe^{x^2} is 2x+2x^3+x^5+1/3 x^7+1/12 x^9+\ldots

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maclaurin 2xe^{x^2}

maclaurin

2 x e^{x^{2}}

2 x + 2 x^{3} + x^{5} + \frac{1}{3} x^{7} + \frac{1}{12} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{120}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1680}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{30240}{9 !} x^{9} + \dots

Refine

= 2 x + 2 x^{3} + x^{5} + \frac{1}{3} x^{7} + \frac{1}{12} x^{9} + \dots

\int x^{3} e^{x y}

\int_{6}^{8} \frac{44}{( x - 6 ) ^{3}} d x

\frac{d}{d x} (- \frac{10}{x ^{3}})

\int_{0}^{\frac{π}{4}} sec^{3} (x) d x

y^{^{'}} + y = cos (x)

What is maclaurin 2xe^{x^2} ?
The answer to maclaurin 2xe^{x^2} is 2x+2x^3+x^5+1/3 x^7+1/12 x^9+\ldots