Physics I / Differentiation rules and composition
Practice question · Match the pairs

Match each differentiation rule to its formula.

  • Power rule
  • Chain rule
  • Quotient rule
  • Product rule
  • d/dx[f(g(x))]d/dx[f(g(x))] = f'(g(x)g(x))⋅g\cdot g'(x)
  • d/dx[f⋅g]d/dx[f\cdot g] = f'g + fg'
  • d/dx[f/g]d/dx[f/g] = (f'g − fg')/g2/g^{2}
  • d/dx[xn]=n⋅xn−1d/dx[x^{n}] = n\cdot x^{n-1}
Hints
  1. Match by structure: sum, product, quotient, or composition.
  2. Only one of these formulas carries a squared denominator.
Show the answer
  • Power rule → d/dx[xn]=n⋅xn−1d/dx[x^{n}] = n\cdot x^{n-1}
  • Chain rule → d/dx[f(g(x))]d/dx[f(g(x))] = f'(g(x)g(x))⋅g\cdot g'(x)
  • Quotient rule → d/dx[f/g]d/dx[f/g] = (f'g − fg')/g2/g^{2}
  • Product rule → d/dx[f⋅g]d/dx[f\cdot g] = f'g + fg'
Why

These four rules cover the differentiation of most elementary expressions.

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