# 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**:

We know that, sec x = 1 / cos x.

Let, u = 1 and v = cos x .

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

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

### Thus, the deivative of sec x is tan x sec x.

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