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Beliebt Rechnen >

derivative f(x)=(x^2-5)e^x

Lösung

ableitung von

f (x) = (x^{2} - 5) e^{x}

Lösung

2 x e^{x} + e^{x} (x^{2} - 5)

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 5) e^{x})

Wende die Produktregel an:

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

f = x^{2} - 5, g = e^{x}

= \frac{d}{d x} (x^{2} - 5) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} - 5)

\frac{d}{d x} (x^{2} - 5) = 2 x

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

= 2 x e^{x} + e^{x} (x^{2} - 5)

Graph

Beliebte Beispiele

(\partial)/(\partial y)(1)

\frac{\partial}{\partial y} (1)

(dx)/(dt)=5x(8-x)

\frac{d x}{d t} = 5 x (8 - x)

derivative of sin(5xln(sin^2(5x)))

\frac{d}{d x} (sin (5 x) ln (sin^{2} (5 x)))

inverselaplace (10)/(s^3+2s^2+20s)

in v erse l a pl a ce \frac{10}{s ^{3} + 2 s ^{2} + 20 s}

integral from 0 to 1 of 0

\int_{0}^{1} 0 d x