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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.
  • 2 worked examples
  • 24 in Derivatives

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)

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Find d/dx[sec²x].

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Common questions

What is the Derivative of sec(x)?

The derivative of secant is secant times tangent. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of sec(x) apply?

The Derivative of sec(x) holds under this condition: x ≠ π/2 + nπ for integer n.

How do you use the Derivative of sec(x)?

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

Practice

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