What is taylor 2xe^{-4x} ?

The answer to taylor 2xe^{-4x} is 2x-8x^2+16x^3-64/3 x^4+64/3 x^5+\ldots

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taylor 2xe^{-4x}

taylor

2 x e^{- 4 x}

2 x - 8 x^{2} + 16 x^{3} - \frac{64}{3} x^{4} + \frac{64}{3} x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 2 x e ^{- 4 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 2 x e ^{- 4 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 2 x e ^{- 4 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{- 16}{2 !} x^{2} + \frac{96}{3 !} x^{3} + \frac{- 512}{4 !} x^{4} + \frac{2560}{5 !} x^{5} + \dots

Refine

= 2 x - 8 x^{2} + 16 x^{3} - \frac{64}{3} x^{4} + \frac{64}{3} x^{5} + \dots

What is taylor 2xe^{-4x} ?
The answer to taylor 2xe^{-4x} is 2x-8x^2+16x^3-64/3 x^4+64/3 x^5+\ldots