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

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

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

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

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derivative

tan (x)

Solution steps

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

Take the constant out:

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

= - \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)

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

Simplify

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

= tan (x)

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