derivative y=x^{sqrt(x)}

Lösung

ableitung von

y = x^{x}

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

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

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

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

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

x \to + π + lim (csc (x))

\frac{d}{d x} ((x - 42)^{2} - 3 x ln ((x - 100)^{2}))

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x

x \to 5 lim (2 x^{2} - 3 x + 4)

d er i v a t i v e - \frac{7 x}{y}