What is maclaurin e^{9x} ?

The answer to maclaurin e^{9x} is 1+9x+81/2 x^2+243/2 x^3+2187/8 x^4+\ldots

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maclaurin e^{9x}

maclaurin

e^{9 x}

1 + 9 x + \frac{81}{2} x^{2} + \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{9 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{9 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{9 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{9}{1 !} x + \frac{81}{2 !} x^{2} + \frac{729}{3 !} x^{3} + \frac{6561}{4 !} x^{4} + \dots

Refine

= 1 + 9 x + \frac{81}{2} x^{2} + \frac{243}{2} x^{3} + \frac{2187}{8} x^{4} + \dots

\frac{1}{3} sin (3 x)

12 x^{3} - 3 y^{2} x^{4} + 1 y^{^{'}} = 0, y (0) = 2

\frac{cos ( x )}{x ^{9}}

\int \frac{1}{u ^{2} - u} d u

x \to - 2 lim (\frac{x ^{3} - 8}{x - 2})

What is maclaurin e^{9x} ?
The answer to maclaurin e^{9x} is 1+9x+81/2 x^2+243/2 x^3+2187/8 x^4+\ldots