# Find the derivative of sec x.

To find the derivative of sec x, we will use the quotient rule.

## Answer: The derivative of sec x is tan x × sec x

Let us see how we can find the derivative of sec x.

**Explanation**:

sec x = 1 / cos x

On differentiating this using the quotient rule, d / dx = (u'v - v'u ) / v^{2 }we get,

Let u = 1 and v = cos x

We know that derivative of constant 1 is 0 and cos x = - sin x

d / dx = sin x / cos^{2 }x

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

As we know sin x / cos x = tan x and 1 / cos x = sec x

d / dx = tan x × sec x