derivative of x*e^{-x^2}

Lösung

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

e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 1 \cdot e^{- x^{2}} + (- 2 e^{- x^{2}} x) x

Vereinfache

1 \cdot e^{- x^{2}} + (- 2 e^{- x^{2}} x) x : e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

= e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

x \to 0 + lim ((tan (6 x))^{2})

\frac{\partial}{\partial x} (x^{5} + y^{7})

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

y^{^{''}} + 9 y = 6 sin (3 t)

d er i v a t i v e 2 sec (x)