rw [Polynomial.derivative_scaleRoots, Algebra.smul_def]
R : Type u_1
inst✝ : CommRing R
p : R[X]
hp : IsCoprime p (derivative p)
r : R
hr : IsUnit r
⊢ IsCoprime (p.scaleRoots r) (derivative (p.scaleRoots r))
R : Type u_1
inst✝ : CommRing R
p : R[X]
hp : IsCoprime p (derivative p)
r : R
hr : IsUnit r
⊢ IsCoprime (p.scaleRoots r)
    ((algebraMap R R[X]) (r ^ (p.natDegree - ((derivative p).natDegree + 1))) * (derivative p).scaleRoots r)