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

The derivative of ln(cos(3x)) is -3tan(3x)

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

The first derivative of ln(cos(3x)) is -3tan(3x)

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derivative of

ln (cos (3 x))

- 3 tan (3 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= \frac{1}{cos ( 3 x )} (- sin (3 x) \cdot 3)

Simplify

\frac{1}{cos ( 3 x )} (- sin (3 x) \cdot 3) : - 3 tan (3 x)

= - 3 tan (3 x)

\frac{d}{d x} (x \cdot e^{- 2 x^{2}})

\int \frac{1}{5 - 3 x} d x

\frac{d}{d x} (- e^{- x} + \frac{1}{3})

\int_{2}^{\infty} - 6 x^{- 2} d x

\int \frac{1}{( x - 6 ) x ^{2} - 12 x} d x

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