CalcRef

Derivatives · Trigonometric

Derivative of cos(x)

ddx[cos⁡x]=−sin⁡x\frac{d}{dx}[\cos x] = -\sin x

The derivative of cosine is negative sine.

Worked examples

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

Answer: -2 sin(2x)

Find d/dx[cos²(x)].
  1. Rewrite as [cos x]². By chain rule: 2 cos x · (-sin x) = -2 sin x cos x = -sin(2x)

Answer: -sin(2x)

Related formulas

Derivative of sin(x)Derivative of tan(x)

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