What is taylor x*cos(2x) ?

The answer to taylor x*cos(2x) is x-2x^3+2/3 x^5-4/45 x^7+2/315 x^9+\ldots

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taylor x*cos(2x)

taylor

x \cdot cos (2 x)

x - 2 x^{3} + \frac{2}{3} x^{5} - \frac{4}{45} x^{7} + \frac{2}{315} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 12}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{80}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 448}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{2304}{9 !} x^{9} + \dots

Refine

= x - 2 x^{3} + \frac{2}{3} x^{5} - \frac{4}{45} x^{7} + \frac{2}{315} x^{9} + \dots

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What is taylor x*cos(2x) ?
The answer to taylor x*cos(2x) is x-2x^3+2/3 x^5-4/45 x^7+2/315 x^9+\ldots