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. Sec x is one of the important and main trigonometric functions in trigonometry. We know that the derivative of secx is equal to secx tanx. We can use the power rule of differentiation and the derivative of sec x to find the derivative of sec square x. In the next section, let us go through the formula for the differentiation of sec^2x. 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. 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.