What is the derivative of ln(cos(2x)) ?

The derivative of ln(cos(2x)) is -2tan(2x)

What is the first derivative of ln(cos(2x)) ?

The first derivative of ln(cos(2x)) is -2tan(2x)

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derivative of

ln (cos (2 x))

- 2 tan (2 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= \frac{1}{cos ( 2 x )} (- sin (2 x) \cdot 2)

Simplify

\frac{1}{cos ( 2 x )} (- sin (2 x) \cdot 2) : - 2 tan (2 x)

= - 2 tan (2 x)

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\int 4 x sin (2 x) d x

What is the derivative of ln(cos(2x)) ?
The derivative of ln(cos(2x)) is -2tan(2x)
What is the first derivative of ln(cos(2x)) ?
The first derivative of ln(cos(2x)) is -2tan(2x)