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Beliebt Rechnen >

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

Lösung

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

Lösung

e^{\frac{x ^{2}}{2}} x^{2} + e^{\frac{x ^{2}}{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = e^{\frac{x ^{2}}{2}}, g = x

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

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

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

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

Vereinfache

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

= e^{\frac{x ^{2}}{2}} x^{2} + e^{\frac{x ^{2}}{2}}

Graph

Beliebte Beispiele

integral of e^{-3y}

\int e^{- 3 y} d y

limit as x approaches 6 of x+6

x \to 6 lim (x + 6)

(d^2)/(dx^2)(1/(3+t))

\frac{d ^{2}}{d x ^{2}} (\frac{1}{3 + t})

tangent f(x)=x^2-x+1

t an g e n t f (x) = x^{2} - x + 1

derivative of 2/3 e^x+e^{-2x}

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