Descartes’ Algebraic Method for Finding Derivatives

Amy DeCelles

In this paper, we discuss Descartes’ algebraic method for finding derivatives, by showing how this method can be used to compute the derivative of f(x)=(Sqrt[x]) at the point (16, 4).

In Descartes’ method, we use first find the circle tangent to the curve at a given point P, then find the equation for the line L connecting the center of the circle to P.  The tangent line will be perpendicular to this line.  See the diagram below.