What is the derivative of ln(1/(cos(x))) ?

The derivative of ln(1/(cos(x))) is tan(x)

What is the first derivative of ln(1/(cos(x))) ?

The first derivative of ln(1/(cos(x))) is tan(x)

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

tan (x)

Solution steps

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

Simplify

ln (\frac{1}{cos ( x )}) : ln (sec (x))

= \frac{d}{d x} (ln (sec (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= \frac{1}{sec ( x )} sec (x) tan (x)

Simplify

\frac{1}{sec ( x )} sec (x) tan (x) : tan (x)

= tan (x)

What is the derivative of ln(1/(cos(x))) ?
The derivative of ln(1/(cos(x))) is tan(x)
What is the first derivative of ln(1/(cos(x))) ?
The first derivative of ln(1/(cos(x))) is tan(x)