History
The chain rule seems to have first been used by Leibniz. He used it to calculate the derivative of as the composite of the square root function and the function . He first mentioned it in a memoir with various mistakes in it. The common notation of chain rule is due to Leibniz. L'Hôpital uses the chain rule implicitly in his Analyse des infiniment petits but also does not state it explicitly. The chain rule does not appear in any of Leonhard Euler's analysis books, even though they were written over a hundred years after Leibniz's discovery.
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