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Popular >

derivative of ln(ln(sec(x)))

Solution

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

Solution

\frac{tan ( x )}{ln ( sec ( x ) )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (sec (x))) = tan (x)

= \frac{1}{ln ( sec ( x ) )} tan (x)

Simplify

\frac{1}{ln ( sec ( x ) )} tan (x) : \frac{tan ( x )}{ln ( sec ( x ) )}

= \frac{tan ( x )}{ln ( sec ( x ) )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(ln(sec(x))) ?
The derivative of ln(ln(sec(x))) is (tan(x))/(ln(sec(x)))
What is the first derivative of ln(ln(sec(x))) ?
The first derivative of ln(ln(sec(x))) is (tan(x))/(ln(sec(x)))