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

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