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

The derivative of ln(sinh(x)) is coth(x)

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

The first derivative of ln(sinh(x)) is coth(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

coth (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= coth (x)

What is the derivative of ln(sinh(x)) ?
The derivative of ln(sinh(x)) is coth(x)
What is the first derivative of ln(sinh(x)) ?
The first derivative of ln(sinh(x)) is coth(x)