What is the derivative of ln(sinh(9x)) ?

The derivative of ln(sinh(9x)) is 9coth(9x)

What is the first derivative of ln(sinh(9x)) ?

The first derivative of ln(sinh(9x)) is 9coth(9x)

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\frac{d}{d x} (ln (sinh (9 x)))

9 coth (9 x)

Solution steps

\frac{d}{d x} (ln (sinh (9 x)))

Apply the chain rule:

\frac{1}{sinh ( 9 x )} \frac{d}{d x} (sinh (9 x))

= \frac{1}{sinh ( 9 x )} \frac{d}{d x} (sinh (9 x))

\frac{d}{d x} (sinh (9 x)) = cosh (9 x) \cdot 9

= \frac{1}{sinh ( 9 x )} cosh (9 x) \cdot 9

Simplify

\frac{1}{sinh ( 9 x )} cosh (9 x) \cdot 9 : 9 coth (9 x)

= 9 coth (9 x)

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (8) = 8

\frac{d}{d x} ((x^{2} + x)^{3})

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

\int_{1}^{2} \frac{11}{x ^{3} + 3 x} d x

\int \frac{1}{x ^{2} \cdot 9 + x ^{2}} d x

What is the derivative of ln(sinh(9x)) ?
The derivative of ln(sinh(9x)) is 9coth(9x)
What is the first derivative of ln(sinh(9x)) ?
The first derivative of ln(sinh(9x)) is 9coth(9x)