taylor cos(2x)

Lösung

taylor

cos (2 x)

1 - 2 x^{2} + \frac{2}{3} x^{4} - \frac{4}{45} x^{6} + \frac{2}{315} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 64}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{256}{8 !} x^{8} + \dots

Fasse zusammen

= 1 - 2 x^{2} + \frac{2}{3} x^{4} - \frac{4}{45} x^{6} + \frac{2}{315} x^{8} + \dots

\frac{\partial}{\partial z} (x^{2} + 2 y + 2 z)

\frac{d}{d x} (\frac{7}{x ^{4}})

x^{2} y^{^{''}} - 11 x y^{^{'}} + 36 y = 0

\frac{\partial}{\partial x} (x sin (4 x^{2} y))

\frac{d}{d x} ((x + \frac{1}{x})^{2})