derivative f(x)=x^2*e^{-x^2}

Lösung

ableitung von

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

2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x e^{- x^{2}} + (- 2 e^{- x^{2}} x) x^{2} : 2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

= 2 e^{- x^{2}} x - 2 e^{- x^{2}} x^{3}

f (x) = \frac{50}{x}

\int y^{\frac{4}{3}} d y

in v erse l a pl a ce \frac{e ^{- 2 s}}{s ^{2} + 16}

\int_{- 1}^{1} \frac{1}{2} (9 - 9 x^{2})^{2} d x

\frac{d}{d x} (500 x - 0.5 x - 500)