What is maclaurin ((2x))/(1+x^4) ?

The answer to maclaurin ((2x))/(1+x^4) is 2x-2x^5+2x^9+\ldots

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maclaurin ((2x))/(1+x^4)

maclaurin

\frac{( 2 x )}{1 + x ^{4}}

2 x - 2 x^{5} + 2 x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( \frac{2 x}{1 + x ^{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{2 x}{1 + x ^{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{2 x}{1 + x ^{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 240}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{725760}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 2 x - 2 x^{5} + 2 x^{9} + \dots

What is maclaurin ((2x))/(1+x^4) ?
The answer to maclaurin ((2x))/(1+x^4) is 2x-2x^5+2x^9+\ldots