derivative x^{8/x}

Lösung

ableitung von

x^{\frac{8}{x}}

8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{8}{x}})

Wende Exponentenregel an:

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

x^{\frac{8}{x}} = e^{\frac{8}{x} l n (x)}

= \frac{d}{d x} (e^{\frac{8}{x} l n (x)})

Wende die Kettenregel an:

e^{\frac{8}{x} l n (x)} \frac{d}{d x} (\frac{8}{x} ln (x))

= e^{\frac{8}{x} l n (x)} \frac{d}{d x} (\frac{8}{x} ln (x))

\frac{d}{d x} (\frac{8}{x} ln (x)) = \frac{8 ( - ln ( x ) + 1 )}{x ^{2}}

= e^{\frac{8}{x} l n (x)} \frac{8 ( - ln ( x ) + 1 )}{x ^{2}}

Vereinfache

e^{\frac{8}{x} l n (x)} \frac{8 ( - ln ( x ) + 1 )}{x ^{2}} : 8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

= 8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

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