What is taylor x*e^x ?

The answer to taylor x*e^x is x+x^2+1/2 x^3+1/6 x^4+1/24 x^5+\ldots

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taylor x*e^x

taylor

x \cdot e^{x}

x + x^{2} + \frac{1}{2} x^{3} + \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{2}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{4}{4 !} x^{4} + \frac{5}{5 !} x^{5} + \dots

Refine

= x + x^{2} + \frac{1}{2} x^{3} + \frac{1}{6} x^{4} + \frac{1}{24} x^{5} + \dots

What is taylor x*e^x ?
The answer to taylor x*e^x is x+x^2+1/2 x^3+1/6 x^4+1/24 x^5+\ldots