What is the derivative of ln(cosh(8x)) ?

The derivative of ln(cosh(8x)) is 8tanh(8x)

What is the first derivative of ln(cosh(8x)) ?

The first derivative of ln(cosh(8x)) is 8tanh(8x)

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\frac{d}{d x} (ln (cosh (8 x)))

8 tanh (8 x)

Solution steps

\frac{d}{d x} (ln (cosh (8 x)))

Apply the chain rule:

\frac{1}{cosh ( 8 x )} \frac{d}{d x} (cosh (8 x))

= \frac{1}{cosh ( 8 x )} \frac{d}{d x} (cosh (8 x))

\frac{d}{d x} (cosh (8 x)) = sinh (8 x) \cdot 8

= \frac{1}{cosh ( 8 x )} sinh (8 x) \cdot 8

Simplify

\frac{1}{cosh ( 8 x )} sinh (8 x) \cdot 8 : 8 tanh (8 x)

= 8 tanh (8 x)

What is the derivative of ln(cosh(8x)) ?
The derivative of ln(cosh(8x)) is 8tanh(8x)
What is the first derivative of ln(cosh(8x)) ?
The first derivative of ln(cosh(8x)) is 8tanh(8x)