Question

What is the slope of the tangent line of `1/y-x^3y-y= C`, where C is an arbitrary constant, at `(1,-2)`?

Answer 1

`m=-24/9`

Explanation:

Differentiate implcitly:

`-1y^(-2) dy/dx -3x^2y-x^3 dy/dx-dy/dx = 0`

Substitute `x=1` and `y=-2`. Then solve for `dy/dx = -24/9`