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Beliebt Rechnen >

(\partial)/(\partial x)(xe^{-x})

Lösung

\frac{\partial}{\partial x} (x e^{- x})

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{- x})

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{- x}) = - e^{- x}

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

Vereinfache

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

Beliebte Beispiele

integral of (9-y)sqrt(y)

\int (9 - y) y d y

sum from n=1 to infinity of (cos(24))^n

n = 1 \sum \infty (cos (24))^{n}

limit as x approaches 0 of (x^2)/2-2/x

x \to 0 lim (\frac{x ^{2}}{2} - \frac{2}{x})

f(x)=arccos(x/2)

f (x) = arccos (\frac{x}{2})

\frac{d}{d y} (x y + y)