maclaurin e^x-e^{-x}

Lösung

maclaurin

e^{x} - e^{- x}

2 x + \frac{1}{3} x^{3} + \frac{1}{60} x^{5} + \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 2 x + \frac{1}{3} x^{3} + \frac{1}{60} x^{5} + \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

d er i v a t i v e - 2 sin (2 x)

x y^{^{'}} + y = 4 x y^{2}

\frac{d}{d x} (\frac{x}{x ^{- 1} + 13})

d er i v a t i v e 2^{50}

x \to 2 π lim (ln (cos (x)))