The slope of a tangent line to a function at a point is actually equal to the derivative of the function at that point.
Slope (m) of the tangent line at (1,1) = dy/dx at (1,1)
Equation of the tangent line can be found by using point slope form
y-y_1 = m(x-x_1)
The normal line is perpendicular to the tangent line
Therefore slope of the normal line = -1/m
Equation of the normal is