What is taylor 2x*e^{2x} ?

The answer to taylor 2x*e^{2x} is 2x+4x^2+4x^3+8/3 x^4+4/3 x^5+\ldots

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taylor 2x*e^{2x}

taylor

2 x \cdot e^{2 x}

2 x + 4 x^{2} + 4 x^{3} + \frac{8}{3} x^{4} + \frac{4}{3} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{8}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{64}{4 !} x^{4} + \frac{160}{5 !} x^{5} + \dots

Refine

= 2 x + 4 x^{2} + 4 x^{3} + \frac{8}{3} x^{4} + \frac{4}{3} x^{5} + \dots

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

\frac{d}{d x} (2 x^{2} - 4 x + 4)

- 8 x^{2} + 500 x + 140

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

\int (2 - x) 4 - x^{2} d x

What is taylor 2x*e^{2x} ?
The answer to taylor 2x*e^{2x} is 2x+4x^2+4x^3+8/3 x^4+4/3 x^5+\ldots