Physics I / Differentiation rules and composition
Practice question · Fill in the blanks

Fill in the key terms about differentiation rules.

The ______ gives d/dx[fg] = f'g + fg'. The ______ gives d/dx[f/g]d/dx[f/g] = (f'g − fg')/g2/g^{2}. For composite functions the ______ multiplies the outer and inner derivatives.

Word bank: product rule · quotient rule · chain rule · power rule

Hints
  1. Each blank names the rule matching one structural pattern.
  2. Look at whether the expression is multiplied, divided, or nested.
Show the answer

The product rule gives d/dx[fg] = f'g + fg'. The quotient rule gives d/dx[f/g]d/dx[f/g] = (f'g − fg')/g2/g^{2}. For composite functions the chain rule multiplies the outer and inner derivatives.

Why

Each rule has a distinct structural pattern for recognising when to apply it.

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