What is maclaurin e^{-5x^4} ?

The answer to maclaurin e^{-5x^4} is 1-5x^4+25/2 x^8+\ldots

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maclaurin e^{-5x^4}

maclaurin

e^{- 5 x^{4}}

1 - 5 x^{4} + \frac{25}{2} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 5 x^{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 5 x^{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 5 x^{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 120}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{504000}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - 5 x^{4} + \frac{25}{2} x^{8} + \dots

\frac{d}{d x} (2^{arcsech (x)})

\int \frac{x}{x ^{4} + 3} d x

\frac{12 s + 8}{( s - 1 ) ^{5}}

\frac{3}{x ^{3}} - \frac{1}{x ^{4}}

(26 \frac{2}{3}, 9), (5, 2.5)

What is maclaurin e^{-5x^4} ?
The answer to maclaurin e^{-5x^4} is 1-5x^4+25/2 x^8+\ldots