maclaurin x/(2x+1)

Lösung

maclaurin

\frac{x}{2 x + 1}

x - 2 x^{2} + 4 x^{3} - 8 x^{4} + 16 x^{5} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 4}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{- 192}{4 !} x^{4} + \frac{1920}{5 !} x^{5} + \dots

Fasse zusammen

= x - 2 x^{2} + 4 x^{3} - 8 x^{4} + 16 x^{5} + \dots

x y^{2} y^{^{'}} = x + 8

\int \frac{2 x}{4 x ^{4} - 9} d x

\frac{d}{d x} (\frac{5}{x + 8})

\int - sin (\frac{1}{2} x) d x

d er i v a t i v e f (x) = 6 cos (x)