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Beliebt Rechnen >

(\partial)/(\partial x)(x^2*e^x)

Lösung

\frac{\partial}{\partial x} (x^{2} \cdot e^{x})

Lösung

2 x e^{x} + e^{x} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Beliebte Beispiele

fläche y=x^2,y= 2/((x^2+1))

a re a y = x^{2}, y = \frac{2}{( x ^{2} + 1 )}

x y^{^{'}} - 4 y = x^{5} e^{x}

(\partial)/(\partial x)(sqrt(9-x^2-3y))

\frac{\partial}{\partial x} (9 - x^{2} - 3 y)

derivative y=arcsin(6x+1)

d er i v a t i v e y = arcsin (6 x + 1)

integral of 1/(sqrt(-2x^2-12x+32))

\int \frac{1}{- 2 x ^{2} - 12 x + 32} d x