Calculus
Intermediate

Derivative of Tangent

Derivative of the tangent function.

Formula

ddxtan⁡x=sec⁡2x\frac{d}{dx}\tan x = \sec^2 x

Variables

xVariable

Example

The slope of tan x at x = 0 is sec²0 = 1.

Did You Know?

The derivative of tan x is sec²x, which is never negative — tangent is always increasing between its asymptotes.

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