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The derivative of sec x with respect to x is written as d/dx(sec x) and it is equal to sec x tan x. Let us learn more about the differentiation of sec x along with its formula, proof by different methods, and a few solved examples. Learn how to differentiate Sec x using the first principle, chain rule and quotient rule. Find the formula for Sec x and its applications in trigonometry and calculus. The derivative of sec x with respect to x is equal to secx tanx. We will prove this by first principle, chain rule and quotient rule of derivatives. Chapter 5 Class 12 Continuity and Differentiability Concept wise Finding derivative of Inverse trigonometric functions