Discover How To Find The Derivative Of Secant X Using The Chain Rule And Simplifying With Trigonometric Identities.

d/dx sec x

tan x sec x

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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