taylor 1/(1+x^3)

Lösung

taylor

\frac{1}{1 + x ^{3}}

1 - x^{3} + x^{6} - x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 362880}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= 1 - x^{3} + x^{6} - x^{9} + \dots

d er i v a t i v e \frac{( 11 ln ( x ) )}{( 2 x + 4 )}

\frac{d y}{d x} = \frac{- x}{y}

f (x) = 3^{x} ln (3)

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 4 x = 2 t

d er i v a t i v e x^{\frac{2}{3}} (1 - x)