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

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

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

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

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

tanh (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= tanh (x)

\frac{\partial}{\partial y} (x cos (y) + y e^{x})

\frac{d}{d x} (\frac{x ^{2} - 1}{2 x})

x \to - 2 lim (\frac{2 - x ^{2}}{4 x})

(x^{2} + 1) (\frac{d y}{d x}) + 3 x (y - 1) = 0, y (0) = 6

\frac{1}{3 ( 4 - x ^{3} ) ^{4}}

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