What is (\partial)/(\partial x)(ln(sec(x))) ?

The answer to (\partial)/(\partial x)(ln(sec(x))) is tan(x)

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(\partial)/(\partial x)(ln(sec(x)))

\frac{\partial}{\partial x} (ln (sec (x)))

tan (x)

Solution steps

\frac{\partial}{\partial x} (ln (sec (x)))

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

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What is (\partial)/(\partial x)(ln(sec(x))) ?
The answer to (\partial)/(\partial x)(ln(sec(x))) is tan(x)