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Popular >

derivative of ln(cos(ln(7x)))

Solution

derivative of

ln (cos (ln (7 x)))

Solution

- \frac{tan ( ln ( 7 x ) )}{x}

Solution steps

\frac{d}{d x} (ln (cos (ln (7 x))))

Apply the chain rule:

\frac{1}{cos ( ln ( 7 x ) )} \frac{d}{d x} (cos (ln (7 x)))

= \frac{1}{cos ( ln ( 7 x ) )} \frac{d}{d x} (cos (ln (7 x)))

\frac{d}{d x} (cos (ln (7 x))) = - \frac{sin ( ln ( 7 x ) )}{x}

= \frac{1}{cos ( ln ( 7 x ) )} (- \frac{sin ( ln ( 7 x ) )}{x})

Simplify

\frac{1}{cos ( ln ( 7 x ) )} (- \frac{sin ( ln ( 7 x ) )}{x}) : - \frac{tan ( ln ( 7 x ) )}{x}

= - \frac{tan ( ln ( 7 x ) )}{x}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(cos(ln(7x))) ?
The derivative of ln(cos(ln(7x))) is -(tan(ln(7x)))/x
What is the first derivative of ln(cos(ln(7x))) ?
The first derivative of ln(cos(ln(7x))) is -(tan(ln(7x)))/x