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Beliebt Rechnen >

derivative of Axe^{x^2}

Lösung

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

Lösung

A (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= A \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}}

= A (\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}}) = e^{x^{2}} \cdot 2 x

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (2sec^2(x)-x^5)

\int (2 sec^{2} (x) - x^{5}) d x

integral of (xsin(y))

\int (x sin (y)) d y

limit as x approaches-5 of 8/((x+5)^6)

x \to - 5 lim (\frac{8}{( x + 5 ) ^{6}})

derivative f(x)=5e^e

d er i v a t i v e f (x) = 5 e^{e}

y^'=(x+y+1)^2,y(0)=0

y^{^{'}} = (x + y + 1)^{2}, y (0) = 0