derivative log_{9}(ln(x))

Lösung

ableitung von

lo g_{9} (ln (x))

\frac{1}{2 ln ( 3 ) x ln ( x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{9} (ln (x)))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( ln ( x ) )}{ln ( 9 )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 9 )} \frac{d}{d x} (ln (ln (x)))

Wende die Kettenregel an:

\frac{1}{ln ( x )} \frac{d}{d x} (ln (x))

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

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

= \frac{1}{ln ( 9 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x}

Vereinfache

\frac{1}{ln ( 9 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x} : \frac{1}{2 ln ( 3 ) x ln ( x )}

= \frac{1}{2 ln ( 3 ) x ln ( x )}

x \to + 0 lim (\frac{8}{6 + e ^{x}})

\int_{1}^{\infty} \frac{3}{x ^{4}} d x

d er i v a t i v e \frac{( 17 - x ) 2 x + 8}{2}

x \to - 1 lim (x^{4} - 2 x^{2} - 1)

\int_{0}^{0.6} (600 x) d x