taylor-2xsin(x^2)

Lösung

taylor

- 2 x sin (x^{2})

- 2 x^{3} + \frac{1}{3} x^{7} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 12}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1680}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= - 2 x^{3} + \frac{1}{3} x^{7} + \dots

\frac{d}{d x} ((sin (x))^{3})

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{2} e^{3 t}

x \to 0 lim (\frac{1 1 ^{x} - 1 0 ^{x}}{x})

d er i v a t i v e G (t) = \frac{4 t}{t + 5}

\frac{d}{d x} (arcsin (3 x - 4 x^{3}))