What is the derivative of log_{3}(sec(2x)) ?

The derivative of log_{3}(sec(2x)) is (2tan(2x))/(ln(3))

What is the first derivative of log_{3}(sec(2x)) ?

The first derivative of log_{3}(sec(2x)) is (2tan(2x))/(ln(3))

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\frac{d}{d x} (lo g_{3} (sec (2 x)))

\frac{2 tan ( 2 x )}{ln ( 3 )}

Solution steps

\frac{d}{d x} (lo g_{3} (sec (2 x)))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( sec ( 2 x ) )}{ln ( 3 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (sec (2 x)))

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 3 )} \cdot \frac{1}{sec ( 2 x )} sec (2 x) tan (2 x) \cdot 2

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{sec ( 2 x )} sec (2 x) tan (2 x) \cdot 2 : \frac{2 tan ( 2 x )}{ln ( 3 )}

= \frac{2 tan ( 2 x )}{ln ( 3 )}

x \to 0 lim (tan (x) - sec (x))

(t e)^{3} e^{- 2 t} e^{- 2}

\frac{d P}{d t} = P (950 - P)

\frac{d y}{d x} = sin (x)

What is the derivative of log_{3}(sec(2x)) ?
The derivative of log_{3}(sec(2x)) is (2tan(2x))/(ln(3))
What is the first derivative of log_{3}(sec(2x)) ?
The first derivative of log_{3}(sec(2x)) is (2tan(2x))/(ln(3))