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Introduction to derivative of inverse secant function formula with proof to learn how to derive differentiation of sec function from first principle in calculus. Here you will learn what is the differentiation of secx and its proof by using first principle. Let’s begin – Differentiation of secx The differentiation of secx ... 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. In this article, we will learn about the derivative of sec x and its formula including the proof of the formula using the first principle of derivatives, quotient rule, and chain rule as well. What is Derivative in Math? The derivative of a function is the rate of change of the function with respect to any independent variable.