Find the derivative w/ respect to x:

g(x) = ln(sec(x))

To find the derivative of the function g(x) = ln(sec(x)), we will use the chain rule. The chain rule states that if we have a composite function, such as ln(f(x)), we first differentiate the outer function, ln(x), and then multiply it by the derivative of the inner function, f'(x).

In this case, the outer function is ln(x), and the inner function is sec(x). Let's start by finding the derivative of the outer function:

The derivative of ln(x) with respect to x is 1/x. Therefore, the derivative of ln(sec(x)) would be 1/sec(x).

Now, let's find the derivative of the inner function, sec(x):

The derivative of sec(x) is sec(x) * tan(x). Therefore, the derivative of sec(x) would be sec(x) * tan(x).

Finally, we multiply the derivative of the outer function by the derivative of the inner function:

g'(x) = (1/sec(x)) * (sec(x) * tan(x)) = tan(x).

Therefore, the derivative of g(x) = ln(sec(x)) with respect to x is tan(x).