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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.
  • 2 worked examples
  • 24 in Derivatives

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)

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Find d/dx[3 cot x].

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Common questions

What is the Derivative of cot(x)?

The derivative of cotangent is negative cosecant squared. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of cot(x) apply?

The Derivative of cot(x) holds under this condition: x ≠ nπ for integer n.

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

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

Practice

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