(\partial)/(\partial x)(x^x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial 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)

x \to \infty lim (9.35 e^{(- 0.4 x)} + 5.52)

x \to - 2 lim (\frac{x ^{2} + 2}{x + 2})

t a y l or \frac{1}{x} lo g_{10} (1 + x)

\frac{\partial}{\partial y} (9 - x^{2} - y^{2})

\frac{d}{d x} (x^{9} + 9^{x})