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Beliebt Rechnen >

derivative of e^{a(e^x-1})

Lösung

\frac{d}{d x} (e^{a (e^{x} - 1)})

Lösung

a e^{a (e^{x} - 1) + x}

Schritte zur Lösung

\frac{d}{d x} (e^{a (e^{x} - 1)})

Wende die Kettenregel an:

e^{a (e^{x} - 1)} \frac{d}{d x} (a (e^{x} - 1))

= e^{a (e^{x} - 1)} \frac{d}{d x} (a (e^{x} - 1))

\frac{d}{d x} (a (e^{x} - 1)) = a e^{x}

= e^{a (e^{x} - 1)} a e^{x}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

e^{a (e^{x} - 1)} e^{x} = e^{a (e^{x} - 1) + x}

= a e^{a (e^{x} - 1) + x}

Graph

Beliebte Beispiele

d er i v a t i v e \frac{1}{s}

fläche y=27-x^2,y=6x,y= 2/5 x

a re a y = 27 - x^{2}, y = 6 x, y = \frac{2}{5} x

tangent sqrt(sin(3x))

t an g e n t sin (3 x)

(dy)/(dx)=3x(x-1)

\frac{d y}{d x} = 3 x (x - 1)

limit as x approaches 0 of 3x^3+6x^2+7x

x \to 0 lim (3 x^{3} + 6 x^{2} + 7 x)