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Formula generalizes chain rule for higher derivatives is termed as

  • A.Faadi Bruno's formula
  • B.Faraday's formula
  • C.Kreyzig's formula
  • D.Leibniz's formula

Answer: A

Faà di Bruno's formula generalises the chain rule to higher derivatives, giving \( \tfrac{d^{n}}{dx^{n}}f(g(x)) \) as a sum over the partitions of \( n \).

The first case is the ordinary chain rule; the second is

\[ (f \circ g)'' = f''(g)\,(g')^{2} + f'(g)\,g'' \]

Leibniz's formula is the analogous generalisation for the product rule, not the chain rule.

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