What is maclaurin e^{(-3x)} ?

The answer to maclaurin e^{(-3x)} is 1-3x+9/2 x^2-9/2 x^3+27/8 x^4+\ldots

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maclaurin e^{(-3x)}

maclaurin

e^{(- 3 x)}

1 - 3 x + \frac{9}{2} x^{2} - \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- 3}{1 !} x + \frac{9}{2 !} x^{2} + \frac{- 27}{3 !} x^{3} + \frac{81}{4 !} x^{4} + \dots

Refine

= 1 - 3 x + \frac{9}{2} x^{2} - \frac{9}{2} x^{3} + \frac{27}{8} x^{4} + \dots

y = \frac{3 x ^{4} + 9}{x ^{2}}

\frac{x ^{3} - 2 x ^{2} + 4}{x ^{2}}

\int (ln (x + 1))^{2} d x

\frac{d}{d x} (2 e^{2 x} cos (x) - e^{2 x} sin (x))

\frac{d}{d x} (e^{12 x - x^{6}})

What is maclaurin e^{(-3x)} ?
The answer to maclaurin e^{(-3x)} is 1-3x+9/2 x^2-9/2 x^3+27/8 x^4+\ldots