derivative f(x)=x^x

Lösung

ableitung von

f (x) = 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)

z \to - 3 lim (\frac{3}{12 - 4 z})

\frac{\partial}{\partial y} (y sin (x) y)

\frac{d}{d x} (x^{2} (6 - x)^{3})

\int \frac{1}{x ^{2} + 8 x + 20} d x

x \to 0 lim (\frac{4}{x} - \frac{4}{∣ x ∣})