derivative of ln(tanh(x))

Lösung

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

sech^{2} (x) coth (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (tanh (x)) = sech^{2} (x)

= \frac{1}{tanh ( x )} sech^{2} (x)

Vereinfache

\frac{1}{tanh ( x )} sech^{2} (x) : sech^{2} (x) coth (x)

= sech^{2} (x) coth (x)

\int 4 cos^{3} (5 x) d x

\frac{\partial}{\partial y} (2 sin (y^{2}))

x \to 5 lim (\frac{sin ( x )}{x})

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\int \frac{x ^{14}}{x ^{5} - 1} d x