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

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

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

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

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derivative of

2 ln (cos (t))

- 2 tan (t)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - 2 tan (t)

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