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Beliebt Rechnen >

derivative of (13x^2-26x+26e^x)

Lösung

\frac{d}{d x} ((13 x^{2} - 26 x + 26) e^{x})

Lösung

13 e^{x} x^{2}

Schritte zur Lösung

\frac{d}{d x} ((13 x^{2} - 26 x + 26) e^{x})

Wende die Produktregel an:

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

f = 13 x^{2} - 26 x + 26, g = e^{x}

= \frac{d}{d x} (13 x^{2} - 26 x + 26) e^{x} + \frac{d}{d x} (e^{x}) (13 x^{2} - 26 x + 26)

\frac{d}{d x} (13 x^{2} - 26 x + 26) = 26 x - 26

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

= (26 x - 26) e^{x} + e^{x} (13 x^{2} - 26 x + 26)

Vereinfache

(26 x - 26) e^{x} + e^{x} (13 x^{2} - 26 x + 26) : 13 e^{x} x^{2}

= 13 e^{x} x^{2}

Graph

Beliebte Beispiele

derivative of e^{x/2}+4x

integral from 0 to 4.5 of 100x

tangent 4x^2-2x,\at x=-1

derivative 1/((1+x)^2)

xy^'=2x^2+y,y(1)=3