Q:

# What is the derivative of secant squared?

A:

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.

## Keep Learning

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).

Sources:

## Related Questions

• A: Logarithmic differentiation refers to the process in calculus of finding the derivative of a function by using the properties of the natural logarithmic fu... Full Answer >
Filed Under:
• A: Lamar University explains that a gradient vector field is a directional derivative that represents the change in the gradient of a function. Gradient field... Full Answer >
Filed Under:
• A: A person can consider a differential equation by determining an initial condition, as a differential equation is an equation that gives the derivative of a... Full Answer >
Filed Under:
• A: The derivative of sine squared is the sine of 2x, expressed as d/dx (sin2(x)) = sin(2x). The derivative function describes the slope of a line at a given p... Full Answer >
Filed Under:
PEOPLE SEARCH FOR