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Beliebt Rechnen >

derivative of log_{6}(cot(8x))

Lösung

\frac{d}{d x} (lo g_{6} (cot (8 x)))

Lösung

- \frac{8 csc ^{2} ( 8 x )}{ln ( 6 ) cot ( 8 x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{6} (cot (8 x)))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( cot ( 8 x ) )}{ln ( 6 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 6 )} \frac{d}{d x} (ln (cot (8 x)))

Wende die Kettenregel an:

\frac{1}{cot ( 8 x )} \frac{d}{d x} (cot (8 x))

= \frac{1}{cot ( 8 x )} \frac{d}{d x} (cot (8 x))

\frac{d}{d x} (cot (8 x)) = - csc^{2} (8 x) \cdot 8

= \frac{1}{ln ( 6 )} \cdot \frac{1}{cot ( 8 x )} (- csc^{2} (8 x) \cdot 8)

Vereinfache

\frac{1}{ln ( 6 )} \cdot \frac{1}{cot ( 8 x )} (- csc^{2} (8 x) \cdot 8) : - \frac{8 csc ^{2} ( 8 x )}{ln ( 6 ) cot ( 8 x )}

= - \frac{8 csc ^{2} ( 8 x )}{ln ( 6 ) cot ( 8 x )}

Graph

Beliebte Beispiele

limit as x approaches 0 of (tan(3x)-sin(3x))/(x^3)

x \to 0 lim (\frac{tan ( 3 x ) - sin ( 3 x )}{x ^{3}})

derivative (x^3)/(6x-3)

d er i v a t i v e \frac{x ^{3}}{6 x - 3}

fläche 3x^2+4,[1,2]

a re a 3 x^{2} + 4, [1, 2]

derivative 160+3.2x-0.03x^2

d er i v a t i v e 160 + 3.2 x - 0.03 x^{2}

derivative of (e^{2x}+e^{-2x}/4)

\frac{d}{d x} (\frac{e ^{2 x} + e ^{- 2 x}}{4})