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

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

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

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

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derivative of

f (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)

sin (x)

y = (arcsin (x^{3}))^{4}

y = 3 x - 2

(1, 1), (4, - 16)

f (x) = e^{- x}

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