posted by DJ .
at the point (1, -6/55)
Use implicit differentiation to find the slope of the tangent line to the curve
y = x^3 - 7x + 9x^2y - 63y
y' = 3x^2 - 7 + 9x^2y' + 18xy - 63y' , where y' = dy/dx
64y' - 9x^2y' = 3x^2 + 18xy-7
y' = dy/dx = (3x^2 + 18xy - 7)/(64 - 9x^2)
I will leave it up to you to do the remaining arithmetic