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Beliebt Rechnen >

derivative x^{10x}

Lösung

ableitung von

x^{10 x}

Lösung

10 x^{10 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{10 x})

Wende Exponentenregel an:

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

x^{10 x} = e^{10 x l n (x)}

= \frac{d}{d x} (e^{10 x l n (x)})

Wende die Kettenregel an:

e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

= e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

\frac{d}{d x} (10 x ln (x)) = 10 (ln (x) + 1)

= e^{10 x l n (x)} \cdot 10 (ln (x) + 1)

e^{10 x l n (x)} = x^{10 x}

= 10 x^{10 x} (ln (x) + 1)

Graph

Beliebte Beispiele

derivative 3x+10

d er i v a t i v e 3 x + 10

integral of (-1/5 sec(1-5x))

\int (- \frac{1}{5} sec (1 - 5 x)) d x

limit as x approaches 1 of (ln(x))^{1-x}

x \to 1 lim ((ln (x))^{1 - x})

integral of e^{14x}

\int e^{14 x} d x

derivative of (x^2+3(x^2-4x))

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 4 x))