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Theorems · Theorem · complex analysis

HasDerivAt.ofReal_comp

∀ {z : ℝ} {f : ℝ → ℝ} {u : ℝ}, HasDerivAt f u z → HasDerivAt (fun y => ↑(f y)) (↑u) z

If a function f : ℝ → ℝ is differentiable at a (real) point x, then it is also differentiable as a function ℝ → ℂ.

Defined in
Mathlib.Analysis.Complex.RealDeriv
Cited by
3 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

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