Derivative of sec x

Differentiate again: \frac{d^2}{dx^2}\left[\sec\left(x\right)\right] = \tan^{2}\left(x\right) \sec\left(x\right) + \sec^{3}\left(x\right).

Plug into the derivative: f'(0.3) = 0.323798. That is the slope of the tangent line there; drag the graph to see it.

\frac{d}{dx}\left[\sec\left(x\right)\right] = \sec\left(x\right) \tan\left(x\right)

sec x = 1/cos x, so the chain rule (or quotient rule) gives sin x / cos²x, which is usually written sec x · tan x.

Trig rule
$\frac{d}{dx}\left[\sec\left(x\right)\right] = \sec\left(x\right) \tan\left(x\right)$

Drag the graph · at x = 0.39 the slope is 0.44443, the height of the dashed curve.

Questions students ask

What is the derivative of sec x?

$\frac{d}{dx}\left[\sec\left(x\right)\right] = \sec\left(x\right) \tan\left(x\right)$ .

What is the second derivative of sec x?

Differentiate again: $\frac{d^2}{dx^2}\left[\sec\left(x\right)\right] = \tan^{2}\left(x\right) \sec\left(x\right) + \sec^{3}\left(x\right)$ .

What is the slope of sec x at x = 0.3?

Plug into the derivative: $f'(0.3) = 0.323798$ . That is the slope of the tangent line there; drag the graph to see it.

How do you find the derivative of sec x?

sec x = 1/cos x, so the chain rule (or quotient rule) gives sin x / cos²x, which is usually written sec x · tan x.

What is the integral of sec x?

See the integral of sec x page for the antiderivative with steps.