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Derivatives · Trigonometric

Derivative of csc(x)

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

The derivative of cosecant is negative cosecant times cotangent.

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

Worked examples

Find d/dx[csc(4x)].
  1. By chain rule: -csc(4x) cot(4x) · 4 = -4 csc(4x) cot(4x)

Answer: -4 csc(4x) cot(4x)

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Find d/dx[5 csc x].

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Common questions

What is the Derivative of csc(x)?

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

When does the Derivative of csc(x) apply?

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

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

Worked example. Find d/dx[csc(4x)]. By chain rule: -csc(4x) cot(4x) · 4 = -4 csc(4x) cot(4x). Answer: -4 csc(4x) cot(4x).

Practice

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