derivative x^x

Lösung

ableitung von

x^{x}

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)

\frac{d}{d x} (\frac{1}{10 x + 11})

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

l a pl a ce t r an s f or m t \cdot 1

\int_{0}^{4} π (x^{2} - 4 x)^{2} d x

\int 5^{c o s (x)} sin (x) d x