Calculus

Can You Differentiate x^x?

Product, quotient, and chain rules, plus log differentiation and the classic x^x problem.

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What to remember

  • Product rule: (fg)' = f'g + fg'. Quotient rule follows from product + chain.
  • Chain rule: derivatives multiply through composition. It is the most-used rule in quant finance.
  • For x^x and friends, take logs first: d/dx x^x = x^x(ln x + 1).
Read the lessonDifferentiation Rules, with a checkpoint at the end.