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Derivatives · Trigonometric

Derivative of tan(x)

ddx[tan⁡x]=sec⁡2x\frac{d}{dx}[\tan x] = \sec^2 x

The derivative of tangent is secant squared.

Conditions. x ≠ π/2 + nπ for integer n.
  • 2 worked examples
  • 24 in Derivatives

Worked examples

Find d/dx[tan(5x)].
  1. By chain rule: sec²(5x) · 5 = 5 sec²(5x)

Answer: 5 sec²(5x)

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Find d/dx[x tan x].

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Related formulas

Derivative of sin(x)Derivative of cos(x)

See all 24 Derivatives formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.

Common questions

What is the Derivative of tan(x)?

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

When does the Derivative of tan(x) apply?

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

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

Worked example. Find d/dx[tan(5x)]. By chain rule: sec²(5x) · 5 = 5 sec²(5x). Answer: 5 sec²(5x).

Practice

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