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Beliebt Vorkalkül >

derivative y=x^x

Lösung

ableitung von

y = x^{x}

Lösung

x^{x} (ln (x) + 1)

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{x} = e^{x l n (x)}

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

Wende die Kettenregel an:

e^{x l n (x)} \frac{d}{d x} (x ln (x))

= e^{x l n (x)} \frac{d}{d x} (x ln (x))

\frac{d}{d x} (x ln (x)) = ln (x) + 1

= e^{x l n (x)} (ln (x) + 1)

e^{x l n (x)} = x^{x}

= x^{x} (ln (x) + 1)

Graph

Beliebte Beispiele

derivative y=ln(2x)

d er i v a t i v e y = ln (2 x)

cartesian (2,(3pi)/2)

c a r t es ian (2, \frac{3 π}{2})

derivative f(x)=5sqrt(x)e^{x^2-3}

d er i v a t i v e f (x) = 5 x e^{x^{2} - 3}

polar (5,5sqrt(3))

p o l a r (5, 53)

gerade (0,3),(2,-3)

l in e (0, 3), (2, - 3)