Maximum value of derivative

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Let $Q^+ := {z ∈ C : Im(z) > 0}$ . Suppose $f$ is analytic on $Q^+$ and $f( Q^+) ⊂ D$ where $D$ is the open unit disc centred at $0$. what can be the maximum value of $|f'(i)|$ ?

Is it ok to use Cauchy's estimate on $B(i,1)$?