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

The derivative of ln(sech(2x)) is -2tanh(2x)

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

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

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

- 2 tanh (2 x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - 2 tanh (2 x)

\int_{\frac{π}{6}}^{π} (sin (x)) d x

\frac{d}{d x} (\frac{x ^{2}}{ln ( x )} + 2 x)

\frac{d}{d x} (e^{- 12 x})

\int (1 - x - y)^{3} d y

(3, - 5), (5, - 5)

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