Learn How to Find the Derivative of Sec x with the Chain Rule and Simplify using Trigonometric Identities

d/dx (sec x)

sec x tan x

We can find the derivative of sec x using the chain rule and the fact that sec x is equal to 1/cos x.

Let y = sec x

Then, y = 1/cos x

Taking the derivative of both sides with respect to x:

dy/dx = d/dx (1/cos x)

Using the chain rule:

dy/dx = -1/(cos x)^2 * (-sin x)

Simplifying:

dy/dx = sin x/(cos x)^2

Therefore, the derivative of sec x is sin x/(cos x)^2.

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