What Is the Derivative of Secant Squared?

The derivative of the function secant squared of x is d/dx(sec^2(x)) = 2sec^2(x)tan(x). This derivative is obtained by applying the chain rule of differentiation and simplifying the result.

Sec^2(x) is a composite function that can be rewritten as (sec(x))^2. The function can be decomposed into its two component functions: h(x) = (g(x))^2 and g(x) = sec(x). To find the derivative, apply the chain rule, which is d/dx(h(g(x)) = h'(g(x))g'(x).

Take the derivative of h(x) = (g(x))^2, which is h'(x) = 2(g(x)), and substitute sec(x) for g(x) to get h'(x) = 2sec(x). Next, multiply h'(x) by the derivative of g(x) = sec(x), which is g'(x) = sec(x)tan(x). Combine the derivatives into d/dx(sec^2(x)) = 2(sec(x))sec(x)tan(x), which can be simplified into d/dx(sec^2(x)) = 2sec^2(x)tan(x).