derivative of (3-4xe^{-2x^2})

Lösung

\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

- 4 e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x (3 - 4 x)

Schritte zur Lösung

\frac{d}{d x} ((3 - 4 x) e^{- 2 x^{2}})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 - 4 x, g = e^{- 2 x^{2}}

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

\frac{d}{d x} (3 - 4 x) = - 4

\frac{d}{d x} (e^{- 2 x^{2}}) = - 4 e^{- 2 x^{2}} x

= (- 4) e^{- 2 x^{2}} + (- 4 e^{- 2 x^{2}} x) (3 - 4 x)

Vereinfache

= - 4 e^{- 2 x^{2}} - 4 e^{- 2 x^{2}} x (3 - 4 x)

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 4 x - 5}{x ^{2}})

x^{2} y^{^{''}} + 5 x y^{^{'}} + 3 y = 0

d er i v a t i v e \frac{7 + 2 x}{9 - 8 x}

\int 15 e^{- 5 x} d x

d u = \frac{1}{x} d x