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Beliebt Rechnen >

derivative of (3x^2-4xe^x)

Lösung

\frac{d}{d x} ((3 x^{2} - 4 x) e^{x})

Lösung

3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 4 x) e^{x})

Wende die Produktregel an:

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

f = 3 x^{2} - 4 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 4 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 4 x)

\frac{d}{d x} (3 x^{2} - 4 x) = 6 x - 4

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

= (6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x)

Vereinfache

(6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x) : 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

= 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

Graph

Beliebte Beispiele

integral of (4x^3-7x-12)/(x^3-x^2-6x)

\int \frac{4 x ^{3} - 7 x - 12}{x ^{3} - x ^{2} - 6 x} d x

derivative of 7/(2x)

\frac{d}{d x} (\frac{7}{2 x})

limit as x approaches-1 of 4x^3+x^2+2x+1

x \to - 1 lim (4 x^{3} + x^{2} + 2 x + 1)

(dy)/(dx)=yx^9sin(x^{10})

\frac{d y}{d x} = y x^{9} sin (x^{10})

derivative of 1/(sqrt(7x))

\frac{d}{d x} (\frac{1}{7 x})