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

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

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

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

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derivative of

- ln (cos (t))

tan (t)

Solution steps

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

Take the constant out:

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

= - \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)

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

Simplify

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

= tan (t)

\frac{\partial}{\partial x} (5 y cos (x))

\int e^{\frac{1}{2} l n (x)} d x

n = 1 \sum \infty \frac{1}{2} (\frac{1}{2})^{n}

y^{^{'}} = \frac{( e ^{x} )}{e ^{y}}, y (0) = 2

n = 0 \sum \infty \frac{1}{n ^{2} + 9 n + 20}

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