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

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

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

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

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derivative of

ln (sec (3 x) + tan (3 x))

3 sec (3 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (3 x) + tan (3 x)) = sec (3 x) tan (3 x) \cdot 3 + sec^{2} (3 x) \cdot 3

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

Simplify

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

= 3 sec (3 x)

\int 2 e^{- 2 x} sin (x) d x

\frac{\partial}{\partial y} (e^{x} ln (y))

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

x^{2} + 4, - x^{2} - 1, [0, 1]

\frac{d y}{d x} = \frac{2 x y + 2 x}{x ^{2} + 1}

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