maclaurin 2e^{-x/2}+e^{-x}

Lösung

maclaurin

2 e^{- \frac{x}{2}} + e^{- x}

3 - 2 x + \frac{3}{4} x^{2} - \frac{5}{24} x^{3} + \frac{3}{64} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 3 - 2 x + \frac{3}{4} x^{2} - \frac{5}{24} x^{3} + \frac{3}{64} x^{4} + \dots

x \to + \frac{π}{2} + lim (e^{s e c (x)})

\frac{d}{d x} (\frac{4 x ^{2} + 2 x + 6}{x})

\int \frac{( ln ( x ) ) ^{40}}{x} d x

\frac{d}{d x} ((\frac{x}{1 + 1 - x ^{2}})^{n})

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