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

The derivative of ln(cosh(2x)) is 2tanh(2x)

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

The first derivative of ln(cosh(2x)) is 2tanh(2x)

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

2 tanh (2 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cosh (2 x)) = sinh (2 x) \cdot 2

= \frac{1}{cosh ( 2 x )} sinh (2 x) \cdot 2

Simplify

\frac{1}{cosh ( 2 x )} sinh (2 x) \cdot 2 : 2 tanh (2 x)

= 2 tanh (2 x)

2 y^{^{''}} + y^{^{'}} - 10 y = 0

\int 3 e^{- 0.8 x} d x

y = 4 x, y = 9 x^{2}

y = 6 e^{x} + \frac{4}{3 x}

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

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