CalcRef

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.

Worked examples

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

Answer: 5 sec²(5x)

Find d/dx[x tan x].
  1. Product rule: (1)(tan x) + (x)(sec²x) = tan x + x sec²x

Answer: tan x + x sec²x

Related formulas

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

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