What is the (cos(ln(x)))^' ?

The (cos(ln(x)))^' is -(sin(ln(x)))/x

What is the first (cos(ln(x)))^' ?

The first (cos(ln(x)))^' is -(sin(ln(x)))/x

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(cos (ln (x)))^{^{'}}

- \frac{sin ( ln ( x ) )}{x}

Solution steps

(cos (ln (x)))^{'}

Apply the chain rule:

- sin (ln (x)) (ln (x))^{'}

= - sin (ln (x)) (ln (x))^{'}

(ln (x))^{'} = \frac{1}{x}

= - sin (ln (x)) \frac{1}{x}

Simplify

- sin (ln (x)) \frac{1}{x} : - \frac{sin ( ln ( x ) )}{x}

= - \frac{sin ( ln ( x ) )}{x}