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I recently noticed that
$\tan{\theta} = \frac{dy}{dx}$
where $\theta$ is the angle of the tangent line to $y(x)$ with respect to the x-axis. Does this relationship have any practical uses, i.e. as a shortcut to finding derivatives, and if not, is there any context this would be useful?
1 Answer
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It is true for linear functions in general. If you have the line $y=mx+b$ the tangent of the angle from the $x$ axis to the line has $\tan \theta=m$. The tangent is just one more straight line.
