# What is the derivative of sec x?

The derivative of any function y = f(x) of a variable x is the rate of change of y with respect to change in x.

## Answer: The derivative of sec x is (sec x tan x).

Let us understand this problem step by step

**Explanation:**

y = sec x = 1 / cos x

As the RHS of this equation is in fraction form, we can use the quotient rule of differentiation

Hence by quotient rule derivative of sec x = 1 / cos x is

d/dx (uv) = (v du/dx − u dv/dx) / v^{2 }------- (1)

u = 1 and v = cos x

Substituting the values of u and v in eqn (1)

d/dx (sec x) = (cos x d/dx (1) − 1 d/dx (cos x)) / (cos x)^{2}

d/dx (sec x) = {0 - (- sin x)} / cos^{2} x

d/dx (sec x) = (sin x / cos^{2} x)

d/dx (sec x) = (sin x / cos x) × (1 / cos x)

d/dx (sec x) = tan x × sec x