Define a tangent y = Ax + B of y = x^2.
we have
x^2 = Ax + B,
x^2 - Ax - B = 0,
because Ax + B is a tangent, there is only one root to this
quadratic equation, so in the quadratic formula
b^2 - 4ac = 0.
which in the formula
leads to
x =-b/2a =-(-A)/2*1
x = A/2
A = 2x.
since in y = Ax + B, A is
the gradient, then
d/dx(x^2) = 2x |