CalcRef

Derivatives · Trigonometric

Derivative of sin(x)

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

The derivative of the sine function is the cosine function.

Worked examples

Find d/dx[sin(3x)].
  1. By chain rule: cos(3x) · 3 = 3 cos(3x)

Answer: 3 cos(3x)

Find d/dx[x sin x].
  1. By product rule: (1)(sin x) + (x)(cos x) = sin x + x cos x

Answer: sin x + x cos x

Related formulas

Derivative of cos(x)Derivative of tan(x)

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