CalcRef

Derivatives · Trigonometric

Derivative of sec(x)

ddx[sec⁡x]=sec⁡xtan⁡x\frac{d}{dx}[\sec x] = \sec x \tan x

The derivative of secant is secant times tangent.

Conditions. x ≠ π/2 + nπ for integer n.

Worked examples

Find d/dx[sec(3x)].
  1. By chain rule: sec(3x) tan(3x) · 3 = 3 sec(3x) tan(3x)

Answer: 3 sec(3x) tan(3x)

Find d/dx[sec²x].
  1. Chain rule: 2 sec x · sec x tan x = 2 sec²x tan x

Answer: 2 sec²x tan x

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