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)

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\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)

\int cos (\frac{nπ x}{2}) d x

\int \frac{( 100 - x ^{2} )}{x} d x

x \to \infty lim (7 e^{x})

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

f (x) = x^{2} e^{2 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)