What is the derivative of ln(sec(3x)) ?

The derivative of ln(sec(3x)) is 3tan(3x)

What is the first derivative of ln(sec(3x)) ?

The first derivative of ln(sec(3x)) is 3tan(3x)

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

3 tan (3 x)

Solution steps

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

Apply the chain rule:

\frac{1}{sec ( 3 x )} \frac{d}{d x} (sec (3 x))

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

\frac{d}{d x} (sec (3 x)) = sec (3 x) tan (3 x) \cdot 3

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

Simplify

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

= 3 tan (3 x)

\frac{d y}{d t} = 0.5 y

G (t) = \frac{4 t}{t + 5}

\frac{d}{d x} (arcsin (3 x - 4 x^{3}))

lo g_{3} (11) p^{3}

y = \frac{5}{x}, (1, 5)

What is the derivative of ln(sec(3x)) ?
The derivative of ln(sec(3x)) is 3tan(3x)
What is the first derivative of ln(sec(3x)) ?
The first derivative of ln(sec(3x)) is 3tan(3x)