Angle between functions

Calculus Level pending

Let there be functions \(f: D \subseteq \mathbb{R} \rightarrow \mathbb{R}\) and \(g: H \subseteq \mathbb{R} \rightarrow \mathbb{R}\) such that there exists \(f'\) and \(g'\) at least at \(x_{0}\). Assume \(f(x_{0}) = g(x_{0})\). Exactly at the point \(\left ( x_{0}, f(x_{0}) \right )\) define the angle between the graphs of \(f\) and \(g\) to be the angle between the tangent vectors to the graphs at that point. Then suppose \(f(x) = \ln(x)\) and \(g(x) = x^{2} - x\). What is the angle between \(f\) and \(g\) in degrees?

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