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

The derivative of sinh(ln(x)) is (cosh(ln(x)))/x

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

The first derivative of sinh(ln(x)) is (cosh(ln(x)))/x

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

\frac{cosh ( ln ( x ) )}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

cosh (ln (x)) \frac{1}{x} : \frac{cosh ( ln ( x ) )}{x}

= \frac{cosh ( ln ( x ) )}{x}

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