The derivative of secant is equal to the tangent of x times the secant of x. Expressed in mathematical terms, the equation reads as d/dx secant(x) = tan(x)sec(x).
A secant can also be expressed as the inverse of its cosine. Using the product rule, the equation can be written as the cosine of x times the derivative of one minus one times the derivative of cosine, all divided by the square of the cosine of x. Simplifying further, the equation becomes one over the cosine of x times the sine of x over the cosine of x. One over the cosine of x is equal to sec(x), and the sine of x over the cosine of x is equal to the tan(x).