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

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

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

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

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derivative of

2 ln (cos (x))

- 2 tan (x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - 2 tan (x)

- \frac{y}{2}

\frac{d}{d x} (tan^{2} (sin (x)) + cos (2 x))

f (x) = arctan (\frac{x}{2})

4 y^{^{''}} = y

x \to \infty lim (e^{5 x})

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