What is the derivative of ln(ln(sec(2x))) ?

The derivative of ln(ln(sec(2x))) is (2tan(2x))/(ln(sec(2x)))

What is the first derivative of ln(ln(sec(2x))) ?

The first derivative of ln(ln(sec(2x))) is (2tan(2x))/(ln(sec(2x)))

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\frac{d}{d x} (ln (ln (sec (2 x))))

\frac{2 tan ( 2 x )}{ln ( sec ( 2 x ) )}

Solution steps

\frac{d}{d x} (ln (ln (sec (2 x))))

Apply the chain rule:

\frac{1}{ln ( sec ( 2 x ) )} \frac{d}{d x} (ln (sec (2 x)))

= \frac{1}{ln ( sec ( 2 x ) )} \frac{d}{d x} (ln (sec (2 x)))

\frac{d}{d x} (ln (sec (2 x))) = 2 tan (2 x)

= \frac{1}{ln ( sec ( 2 x ) )} \cdot 2 tan (2 x)

Simplify

\frac{1}{ln ( sec ( 2 x ) )} \cdot 2 tan (2 x) : \frac{2 tan ( 2 x )}{ln ( sec ( 2 x ) )}

= \frac{2 tan ( 2 x )}{ln ( sec ( 2 x ) )}

What is the derivative of ln(ln(sec(2x))) ?
The derivative of ln(ln(sec(2x))) is (2tan(2x))/(ln(sec(2x)))
What is the first derivative of ln(ln(sec(2x))) ?
The first derivative of ln(ln(sec(2x))) is (2tan(2x))/(ln(sec(2x)))