What is maclaurin e^{6x} ?

The answer to maclaurin e^{6x} is 1+6x+18x^2+36x^3+54x^4+\ldots

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maclaurin e^{6x}

maclaurin

e^{6 x}

1 + 6 x + 18 x^{2} + 36 x^{3} + 54 x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{6 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{6 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{6 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{6}{1 !} x + \frac{36}{2 !} x^{2} + \frac{216}{3 !} x^{3} + \frac{1296}{4 !} x^{4} + \dots

Refine

= 1 + 6 x + 18 x^{2} + 36 x^{3} + 54 x^{4} + \dots

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

\int_{0}^{1} (6 x + 1) d x

\int 3 x (cos (4 x)) d x

\int cos (x^{4} + 2) d x

\frac{d y}{d x} = \frac{y}{10} (500 - y)

What is maclaurin e^{6x} ?
The answer to maclaurin e^{6x} is 1+6x+18x^2+36x^3+54x^4+\ldots