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Why is the LeibnitzLeibniz rule a definition for derivations?

In differential geometry, the tangent space is defined as a generalization of directional derivatives, which in turn are defined as functionals following Leibnitz'sLeibniz's product rule.

I understand all the proofs, but what is the intuition behind choosing the product rule to capture the notion of derivatives, rather than any other property?

Why is the Leibnitz rule a definition for derivations?

In differential geometry, the tangent space is defined as a generalization of directional derivatives, which in turn are defined as functionals following Leibnitz's product rule.

I understand all the proofs, but what is the intuition behind choosing the product rule to capture the notion of derivatives, rather than any other property?

Why is the Leibniz rule a definition for derivations?

In differential geometry, the tangent space is defined as a generalization of directional derivatives, which in turn are defined as functionals following Leibniz's product rule.

I understand all the proofs, but what is the intuition behind choosing the product rule to capture the notion of derivatives, rather than any other property?

Source Link
R S
R S
  • 995
  • 1
  • 11
  • 14

Why is the Leibnitz rule a definition for derivations?

In differential geometry, the tangent space is defined as a generalization of directional derivatives, which in turn are defined as functionals following Leibnitz's product rule.

I understand all the proofs, but what is the intuition behind choosing the product rule to capture the notion of derivatives, rather than any other property?