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Beliebt Rechnen >

derivative of ax^2e^{-x}

Lösung

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

Lösung

a (2 e^{- x} x - e^{- x} x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative of ln(3/(x^2+9))

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))

tangent f(x)=x^x,\at x=2

t an g e n t f (x) = x^{x}, at x = 2

(xy^2-x)dx+(x^2y+y)dy=0

(x y^{2} - x) d x + (x^{2} y + y) d y = 0

(\partial)/(\partial x)(20-2x+1.5-x+3x)

\frac{\partial}{\partial x} (20 - 2 x + 1.5 - x + 3 x)

(d^2}{dx^2}(-8sin(\frac{3x)/2+1))

\frac{d ^{2}}{d x ^{2}} (- 8 sin (\frac{3 x}{2} + 1))