derivative of log_{5}(tan(x))

Lösung

\frac{d}{d x} (lo g_{5} (tan (x)))

\frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{5} (tan (x)))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( tan ( x ) )}{ln ( 5 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (tan (x)))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= \frac{1}{ln ( 5 )} \cdot \frac{1}{tan ( x )} sec^{2} (x)

Vereinfache

\frac{1}{ln ( 5 )} \cdot \frac{1}{tan ( x )} sec^{2} (x) : \frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

= \frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

x \to 4 - lim (c x^{2} + 3 x)

\int 2 x^{3} - 20 x^{- 5} d x

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

\frac{d}{d x} (4 x + \frac{3}{x})

in v erse l a pl a ce \frac{e ^{- s}}{s ^{2} + 1}