CalcRef

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.

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)

Find d/dx[5 csc x].
  1. 5 · (-csc x cot x) = -5 csc x cot x

Answer: -5 csc x cot x

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