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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.

  • 2 worked examples
  • 24 in Derivatives

Worked examples

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

Answer: 3x² + 4

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Find d/dx[x² - sin x].

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Common questions

What is the Sum/Difference Rule?

The derivative of a sum or difference is the sum or difference of the derivatives. It is one of the derivatives formulas in the CalcRef reference.

How do you use the Sum/Difference Rule?

Worked example. Find d/dx[x³ + 4x]. d/dx[x³] + d/dx[4x] = 3x² + 4. Answer: 3x² + 4.

Practice

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