derivative x^{1-x}

Lösung

ableitung von

x^{1 - x}

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

Schritte zur Lösung

\frac{d}{d x} (x^{1 - x})

Wende Exponentenregel an:

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

x^{1 - x} = e^{(1 - x) l n (x)}

= \frac{d}{d x} (e^{(1 - x) l n (x)})

Wende die Kettenregel an:

e^{(1 - x) l n (x)} \frac{d}{d x} ((1 - x) ln (x))

= e^{(1 - x) l n (x)} \frac{d}{d x} ((1 - x) ln (x))

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

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

e^{(1 - x) l n (x)} = x^{1 - x}

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

d er i v a t i v e \frac{z - 1}{x ^{3}}

d er i v a t i v e y = (x - 1) (x - 2)

d er i v a t i v e 6 x + 457

d er i v a t i v e \frac{x ^{5}}{3}

d er i v a t i v e (\frac{1 - 2 x}{1 + x})^{3}