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

The derivative of ln(sinh(5x)) is 5coth(5x)

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

The first derivative of ln(sinh(5x)) is 5coth(5x)

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

5 coth (5 x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 5 coth (5 x)

y = (3 x - 2 x^{2})^{3}

\frac{9 + 6 x}{7 - 4 x}

y = e^{x} (p + p p)

ln (2 - 3 x)

\frac{d y}{d x} = \frac{x sec ( \frac{y}{x} ) + y}{x}

What is the derivative of ln(sinh(5x)) ?
The derivative of ln(sinh(5x)) is 5coth(5x)
What is the first derivative of ln(sinh(5x)) ?
The first derivative of ln(sinh(5x)) is 5coth(5x)