# 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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