CalcRef

Derivatives · Basic Rules

Constant Multiple Rule

ddx[c⋅f(x)]=c⋅f′(x)\frac{d}{dx}[c \cdot f(x)] = c \cdot f'(x)

A constant factor passes through the derivative operator.

Worked examples

Find d/dx[5x³].
  1. 5 · d/dx[x³] = 5 · 3x² = 15x²

Answer: 15x²

Find d/dx[-3 sin x].
  1. -3 · d/dx[sin x] = -3 cos x

Answer: -3 cos x

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