derivative of x^{-ln(x})

Lösung

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

- \frac{2 e ^{- l n^{2} (x)} ln ( x )}{x}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} ((- ln (x)) ln (x)) = - \frac{2 ln ( x )}{x}

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

Vereinfache

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

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

\int sin^{2} (2 t) cos (2 t) d t

x \to 5 lim (x 41 - x^{2})

\frac{d}{d x} (- 64 cos (4 x))

\int \frac{sin ( 2 x )}{36 + cos ^{2} ( x )} d x

0.5 q^{^{''}} + 10 q^{^{'}} + 100 q = 150