taylor sin(x+pi)

Lösung

taylor

sin (x + π)

- x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= - x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

l a pl a ce t r an s f or m 2 e^{- 4 t}

\frac{d}{d x} (ln (\frac{y}{x}))

\frac{\partial}{\partial y} (x^{2} - 2 x - x y)

d er i v a t i v e \frac{x ^{2}}{( x ^{2} - 1 ) ^{4}}

\frac{\partial}{\partial y} (x^{2} e^{y})