B Can you deduce ##\tan(\theta) = \frac {df} {dx}## from this graph?

I_laff
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Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##.
Thanks

upload_2018-6-11_11-55-30.png
 

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Draw a vertical line going through point P and consider the triangle made by P, the intersection of the vertical line with the x-axis and the intersection of the tangent with the x axis. Then take into account that a tangent has the same derivative as the function at the point where it touches the function (by definition).
 
I think it's by definition that CP and CQ are the same, line p denotes the circle, which has rise/slide df/dx as sin/cos which is tangent of the angle at P, which is the same angle as the dotted line makes with the x axis. If line p wasn't a radius, the slope would not be tan.
 

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