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)

x \to \infty lim (arctan (x))

\frac{d}{d x} (\frac{sin ( x ^{3} )}{x ^{2}})

- 2 t^{3} δ (t - 4)

y^{^{''}} + 3 y^{^{'}} + y = (2 - 6 x) cos (x) - 9 sin (x)

x \to 0 lim (x^{- x})

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)