What is taylor 6xe^x ?

The answer to taylor 6xe^x is 6x+6x^2+3x^3+x^4+1/4 x^5+\ldots

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taylor 6xe^x

taylor

6 x e^{x}

6 x + 6 x^{2} + 3 x^{3} + x^{4} + \frac{1}{4} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{6}{1 !} x + \frac{12}{2 !} x^{2} + \frac{18}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{30}{5 !} x^{5} + \dots

Refine

= 6 x + 6 x^{2} + 3 x^{3} + x^{4} + \frac{1}{4} x^{5} + \dots

10 (x^{3} - x)^{4}

\frac{d}{d x} (sin (9 cos (x)))

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

x \to - \infty lim (\frac{- 1}{x})

\int \frac{1}{x ^{2} 9 x ^{2} - 4} d x

What is taylor 6xe^x ?
The answer to taylor 6xe^x is 6x+6x^2+3x^3+x^4+1/4 x^5+\ldots