Differentiable function/D in R/Rules/Fact

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Let be a subset, a point, and

functions which are differentiable in . Then the following rules for differentiability holds.

  1. The sum is differentiable in , with
  2. The product is differentiable in , with
  3. For , also is differentiable in , with
  4. If has no zero in , then is differentiable in , with
  5. If has no zero in , then is differentiable in , with