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Derivatives · Basic Rules

Sum/Difference Rule

ddx[f(x)±g(x)]=f′(x)±g′(x)\frac{d}{dx}[f(x) \pm g(x)] = f'(x) \pm g'(x)

The derivative of a sum or difference is the sum or difference of the derivatives.

Worked examples

Find d/dx[x³ + 4x].
  1. d/dx[x³] + d/dx[4x] = 3x² + 4

Answer: 3x² + 4

Find d/dx[x² - sin x].
  1. d/dx[x²] - d/dx[sin x] = 2x - cos x

Answer: 2x - cos x

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