derivative_C_mul_X_pow — Mathlib

English

For any f ∈ R[X], d.compAEval a f = derivative f · AEval.of R M a (d a).

Русский

Для любого f ∈ R[X] выполняется d.compAEval a f = derivative f · AEval.of R M a (d a).

LaTeX

$$$d\\cdot\\mathrm{compAEval}(a)(f) = \\operatorname{derivative}(f) \\cdot \\mathrm{AEval.of}\\ R\\; M\\ a\\bigl(d a\\bigr).$$$

Lean4

theorem derivative_C_mul_X_pow (a : R) (n : ℕ) : derivative (C a * X ^ n) = C (a * n) * X ^ (n - 1) := by
  rw [C_mul_X_pow_eq_monomial, C_mul_X_pow_eq_monomial, derivative_monomial]

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