What is maclaurin te^{6t} ?

The answer to maclaurin te^{6t} is t+6t^2+18t^3+36t^4+54t^5+\ldots

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maclaurin te^{6t}

maclaurin

t e^{6 t}

t + 6 t^{2} + 18 t^{3} + 36 t^{4} + 54 t^{5} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} t + \frac{12}{2 !} t^{2} + \frac{108}{3 !} t^{3} + \frac{864}{4 !} t^{4} + \frac{6480}{5 !} t^{5} + \dots

Refine

= t + 6 t^{2} + 18 t^{3} + 36 t^{4} + 54 t^{5} + \dots

\frac{d}{d x} (8 x^{2} + 14 x y + 5 y^{2})

(9, 7), (6, - 2)

\frac{3 x ^{4} + 6}{x ^{2}}

y = e^{6}

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

What is maclaurin te^{6t} ?
The answer to maclaurin te^{6t} is t+6t^2+18t^3+36t^4+54t^5+\ldots