maclaurin e^{-4x}

Lösung

maclaurin

e^{- 4 x}

1 - 4 x + 8 x^{2} - \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{- 4 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- 4 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- 4 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 4}{1 !} x + \frac{16}{2 !} x^{2} + \frac{- 64}{3 !} x^{3} + \frac{256}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - 4 x + 8 x^{2} - \frac{32}{3} x^{3} + \frac{32}{3} x^{4} + \dots

\int 5 - 4 x - x^{2} d x

\int_{0}^{a} a^{2} - x^{2} d x

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

d er i v a t i v e f (x) = 3 x

d er i v a t i v e x^{2} - 5 x - 1