Using the chain rule, we can find the derivative of `sec x` as follows:
`d/dx sec x = d/dx (1/cos x)`
`= -1/cos x * d/dx (cos x)`
`= -1/cos x * (-sin x)`
`= sin x / cos x^2`
We can simplify this expression by using the identity `tan x = sin x / cos x`, and expressing the derivative in terms of `tan x` as:
`d/dx sec x = sin x / cos x^2 = tan x sec x`
Therefore, the derivative of `sec x` with respect to `x` is `tan x sec x`.
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