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Beliebt Rechnen >

derivative of Ax^2e^x

Lösung

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

Lösung

A (2 x e^{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})

Graph

Beliebte Beispiele

integral from 0 to 3 of 450.268e^{1.12567t}

\int_{0}^{3} 450.268 e^{1.12567 t} d t

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

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

derivative 2e^xcos(x)

d er i v a t i v e 2 e^{x} cos (x)

(\partial)/(\partial x)(ln(x^3))

\frac{\partial}{\partial x} (ln (x^{3}))

integral of 1/((1-y))

\int \frac{1}{( 1 - y )} d y