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Popular Calculus >

derivative of ln(ln(sec(2x)))

Solution

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

Solution

\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 ) )}

Graph

Popular Examples

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(du+2dv)/(u+2v)=0

\frac{d u + 2 d v}{u + 2 v} = 0

limit as x approaches 2 of 3x^2-2x+1

x \to 2 lim (3 x^{2} - 2 x + 1)

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Frequently Asked Questions (FAQ)

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)))