What is the derivative of ln(cosh(5x)) ?

The derivative of ln(cosh(5x)) is 5tanh(5x)

What is the first derivative of ln(cosh(5x)) ?

The first derivative of ln(cosh(5x)) is 5tanh(5x)

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\frac{d}{d x} (ln (cosh (5 x)))

5 tanh (5 x)

Solution steps

\frac{d}{d x} (ln (cosh (5 x)))

Apply the chain rule:

\frac{1}{cosh ( 5 x )} \frac{d}{d x} (cosh (5 x))

= \frac{1}{cosh ( 5 x )} \frac{d}{d x} (cosh (5 x))

\frac{d}{d x} (cosh (5 x)) = sinh (5 x) \cdot 5

= \frac{1}{cosh ( 5 x )} sinh (5 x) \cdot 5

Simplify

\frac{1}{cosh ( 5 x )} sinh (5 x) \cdot 5 : 5 tanh (5 x)

= 5 tanh (5 x)

\frac{d}{d x} (\frac{4 + x}{x e ^{x}})

\int \frac{1}{3} e^{t} d t

f (x) = ln (\frac{5 x + 3}{5 x - 3})

x^{2} + x \frac{d y}{d x} = y

\frac{\partial}{\partial y} (- 3 y)

What is the derivative of ln(cosh(5x)) ?
The derivative of ln(cosh(5x)) is 5tanh(5x)
What is the first derivative of ln(cosh(5x)) ?
The first derivative of ln(cosh(5x)) is 5tanh(5x)