What is maclaurin x/(e^x) ?

The answer to maclaurin x/(e^x) is x-x^2+1/2 x^3-1/6 x^4+1/24 x^5+\ldots

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maclaurin x/(e^x)

maclaurin

\frac{x}{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 Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( \frac{x}{e ^{x}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x}{e ^{x}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{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 maclaurin x/(e^x) ?
The answer to maclaurin x/(e^x) is x-x^2+1/2 x^3-1/6 x^4+1/24 x^5+\ldots