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Beliebt Rechnen >

derivative of (e^{x^2}/2)

Lösung

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

Lösung

e^{x^{2}} x

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (e^{x^{2}})

Wende die Kettenregel an:

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

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

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

= \frac{1}{2} e^{x^{2}} \cdot 2 x

Vereinfache

\frac{1}{2} e^{x^{2}} \cdot 2 x : e^{x^{2}} x

= e^{x^{2}} x

Graph

Beliebte Beispiele

derivative log_{10}(n)

d er i v a t i v e lo g_{10} (n)

integral of (4x+1)/((2x^2+x)^5)

\int \frac{4 x + 1}{( 2 x ^{2} + x ) ^{5}} d x

(\partial)/(\partial x)(8x^2+14xy+5y^2)

\frac{\partial}{\partial x} (8 x^{2} + 14 x y + 5 y^{2})

tangent x^2+y^2=25,(4,3)

t an g e n t x^{2} + y^{2} = 25, (4, 3)

integral of-2/(x^2+1)

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