What is taylor-2sin(4x) ?

The answer to taylor-2sin(4x) is -8x+64/3 x^3-256/15 x^5+2048/315 x^7-4096/2835 x^9+\ldots

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taylor-2sin(4x)

taylor

- 2 sin (4 x)

- 8 x + \frac{64}{3} x^{3} - \frac{256}{15} x^{5} + \frac{2048}{315} x^{7} - \frac{4096}{2835} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{- 8}{1 !} x + \frac{0}{2 !} x^{2} + \frac{128}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 2048}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{32768}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 524288}{9 !} x^{9} + \dots

Refine

= - 8 x + \frac{64}{3} x^{3} - \frac{256}{15} x^{5} + \frac{2048}{315} x^{7} - \frac{4096}{2835} x^{9} + \dots

What is taylor-2sin(4x) ?
The answer to taylor-2sin(4x) is -8x+64/3 x^3-256/15 x^5+2048/315 x^7-4096/2835 x^9+\ldots