What is the derivative of ln(tanh(2x)) ?

The derivative of ln(tanh(2x)) is 2sech^2(2x)coth(2x)

What is the first derivative of ln(tanh(2x)) ?

The first derivative of ln(tanh(2x)) is 2sech^2(2x)coth(2x)

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

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

Solution steps

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

Apply the chain rule:

\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

Simplify

\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)

What is the derivative of ln(tanh(2x)) ?
The derivative of ln(tanh(2x)) is 2sech^2(2x)coth(2x)
What is the first derivative of ln(tanh(2x)) ?
The first derivative of ln(tanh(2x)) is 2sech^2(2x)coth(2x)