derivative of ln(tanh(2x))

Lösung

\frac{d}{d x} (ln (tanh (2 x)))

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

Schritte zur Lösung

\frac{d}{d x} (ln (tanh (2 x)))

Wende die Kettenregel an:

\frac{1}{tanh ( 2 x )} \frac{d}{d x} (tanh (2 x))

= \frac{1}{tanh ( 2 x )} \frac{d}{d x} (tanh (2 x))

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

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

Vereinfache

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

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

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

x \to - 4 - lim (\frac{1}{x + 4})

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1, y (1) = 0

d er i v a t i v e \frac{1}{7 x}

\frac{\partial}{\partial x} (sin (8 π t + 9 x))