Geometric interpretation of the derivative

Geometrically, the derivative of a function $f(x)$ at a given point is the slope of the tangent to $f(x)$ at the point $a$.

(See the figure to understand it).

The straight line forms a certain angle that we call $\beta$.

Obviously, this angle will be related to the slope of the straight line, which we have said to be the value of the derivative at the given point.

So we have $$\tan \beta =f^{\prime }(a)$$