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Beliebt Rechnen >

derivative of x^2e^{x+3}

Lösung

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

Lösung

2 x e^{x + 3} + e^{x + 3} x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = e^{x + 3}

= \frac{d}{d x} (x^{2}) e^{x + 3} + \frac{d}{d x} (e^{x + 3}) x^{2}

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

\frac{d}{d x} (e^{x + 3}) = e^{x + 3}

= 2 x e^{x + 3} + e^{x + 3} x^{2}

Graph

Beliebte Beispiele

y^{''}-2y^'+y=1

y^{^{''}} - 2 y^{^{'}} + y = 1

(dy)/(dx)=(x^2+y^2)/(yx)

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{y x}

derivative ln(x+9)

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limit as t approaches 0 of e^{-3t}

t \to 0 lim (e^{- 3 t})

derivative of ax^2e^{4x}

\frac{d}{d x} (a x^{2} e^{4 x})