What is the derivative of ln(cosh(4x)) ?

The derivative of ln(cosh(4x)) is 4tanh(4x)

What is the first derivative of ln(cosh(4x)) ?

The first derivative of ln(cosh(4x)) is 4tanh(4x)

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\frac{d}{d x} (ln (cosh (4 x)))

4 tanh (4 x)

Solution steps

\frac{d}{d x} (ln (cosh (4 x)))

Apply the chain rule:

\frac{1}{cosh ( 4 x )} \frac{d}{d x} (cosh (4 x))

= \frac{1}{cosh ( 4 x )} \frac{d}{d x} (cosh (4 x))

\frac{d}{d x} (cosh (4 x)) = sinh (4 x) \cdot 4

= \frac{1}{cosh ( 4 x )} sinh (4 x) \cdot 4

Simplify

\frac{1}{cosh ( 4 x )} sinh (4 x) \cdot 4 : 4 tanh (4 x)

= 4 tanh (4 x)

\int tan^{2} (2 y) d y

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

x \to \infty lim (3 x - 1)

t \to 0 lim (\frac{sin ( 3 t )}{t} + 2)

\int 4 x e^{5 x} d x

What is the derivative of ln(cosh(4x)) ?
The derivative of ln(cosh(4x)) is 4tanh(4x)
What is the first derivative of ln(cosh(4x)) ?
The first derivative of ln(cosh(4x)) is 4tanh(4x)