derivative of (ln(x)^{sec(x)})

Lösung

\frac{d}{d x} ((ln (x))^{s e c (x)})

ln^{s e c (x)} (x) (sec (x) tan (x) ln (ln (x)) + \frac{sec ( x )}{x ln ( x )})

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{s e c (x)})

Wende Exponentenregel an:

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

(ln (x))^{s e c (x)} = e^{s e c (x) l n (l n (x))}

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

Wende die Kettenregel an:

e^{s e c (x) l n (l n (x))} \frac{d}{d x} (sec (x) ln (ln (x)))

= e^{s e c (x) l n (l n (x))} \frac{d}{d x} (sec (x) ln (ln (x)))

\frac{d}{d x} (sec (x) ln (ln (x))) = sec (x) tan (x) ln (ln (x)) + \frac{sec ( x )}{x ln ( x )}

= e^{s e c (x) l n (l n (x))} (sec (x) tan (x) ln (ln (x)) + \frac{sec ( x )}{x ln ( x )})

e^{s e c (x) l n (l n (x))} = ln^{s e c (x)} (x)

= ln^{s e c (x)} (x) (sec (x) tan (x) ln (ln (x)) + \frac{sec ( x )}{x ln ( x )})

\frac{\partial}{\partial y} (x \cdot y^{2} \cdot e^{z})

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\int e^{x} \cdot ln (x) d x

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x \to 0 lim (\frac{x ^{3} + 7 x}{x})