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Beliebt Rechnen >

derivative x^{2*x}

Lösung

ableitung von

x^{2 \cdot x}

Lösung

2 x^{2 x} (ln (x) + 1)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

x^{2 x} = e^{2 x l n (x)}

= \frac{d}{d x} (e^{2 x l n (x)})

Wende die Kettenregel an:

e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

= e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

\frac{d}{d x} (2 x ln (x)) = 2 (ln (x) + 1)

= e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

e^{2 x l n (x)} = x^{2 x}

= 2 x^{2 x} (ln (x) + 1)

Graph

Beliebte Beispiele

derivative y=(x^4+5x^2)^7

d er i v a t i v e y = (x^{4} + 5 x^{2})^{7}

derivative y-x^2+1

d er i v a t i v e y - x^{2} + 1

\frac{d}{d t} (50 + 4 t)

derivative 3-2x+4x^2

d er i v a t i v e 3 - 2 x + 4 x^{2}

derivative 9e^{-3}x^2

d er i v a t i v e 9 e^{- 3} x^{2}