CalcRef

Derivatives · Trigonometric

Derivative of cot(x)

ddx[cot⁡x]=−csc⁡2x\frac{d}{dx}[\cot x] = -\csc^2 x

The derivative of cotangent is negative cosecant squared.

Conditions. x ≠ nπ for integer n.

Worked examples

Find d/dx[cot(x/2)].
  1. By chain rule: -csc²(x/2) · (1/2) = -(1/2) csc²(x/2)

Answer: -(1/2) csc²(x/2)

Find d/dx[3 cot x].
  1. 3 · (-csc²x) = -3 csc²x

Answer: -3 csc²x

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