What is taylor xe^{x^2} ?

The answer to taylor xe^{x^2} is x+x^3+1/2 x^5+1/6 x^7+1/24 x^9+\ldots

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taylor xe^{x^2}

taylor

x e^{x^{2}}

x + x^{3} + \frac{1}{2} x^{5} + \frac{1}{6} x^{7} + \frac{1}{24} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{60}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{840}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{15120}{9 !} x^{9} + \dots

Refine

= x + x^{3} + \frac{1}{2} x^{5} + \frac{1}{6} x^{7} + \frac{1}{24} x^{9} + \dots

\int 6 x^{- 7} d x

f (x) = (1 + 4 x^{2}) (x - x^{2})

y = (1 + 2 x)^{9}

2 x^{\frac{1}{2}}

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

What is taylor xe^{x^2} ?
The answer to taylor xe^{x^2} is x+x^3+1/2 x^5+1/6 x^7+1/24 x^9+\ldots