lemma
proved
tactic proof
hasDerivAt_Jlog
show as:
view Lean formalization →
formal statement (Lean)
180lemma hasDerivAt_Jlog (t : ℝ) : HasDerivAt Jlog (Real.sinh t) t := by
proof body
Tactic-mode proof.
181 have h1 : Jlog = fun t => Real.cosh t - 1 := by
182 ext t
183 exact Jlog_as_cosh t
184 rw [h1]
185 have h_cosh : HasDerivAt Real.cosh (Real.sinh t) t := Real.hasDerivAt_cosh t
186 have h_const : HasDerivAt (fun _ => (1 : ℝ)) 0 t := hasDerivAt_const t 1
187 have h_sub := h_cosh.sub h_const
188 simp at h_sub
189 exact h_sub
190