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Beliebt Rechnen >

derivative of e^x(x-9)

Lösung

\frac{d}{d x} (e^{x} (x - 9))

Lösung

e^{x} x - 8 e^{x}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (x - 9))

Wende die Produktregel an:

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

f = e^{x}, g = x - 9

= \frac{d}{d x} (e^{x}) (x - 9) + \frac{d}{d x} (x - 9) e^{x}

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

\frac{d}{d x} (x - 9) = 1

= e^{x} (x - 9) + 1 \cdot e^{x}

Vereinfache

e^{x} (x - 9) + 1 \cdot e^{x} : e^{x} x - 8 e^{x}

= e^{x} x - 8 e^{x}

Graph

Beliebte Beispiele

derivative of (x^5+5/(x^3))

\frac{d}{d x} (\frac{x ^{5} + 5}{x ^{3}})

fläche 4x^2+10,2x+7,-3,2

a re a 4 x^{2} + 10, 2 x + 7, - 3, 2

derivative of 3x^2+1/(x^2)

\frac{d}{d x} (3 x^{2} + \frac{1}{x ^{2}})

integral of-1/(x-4)

\int - \frac{1}{x - 4} d x

tangent 4x-32sqrt(x),\at x=4

t an g e n t 4 x - 32 x, at x = 4