Question

What is the derivative of `(x^3)-(xy)+(y^3)=1`?

Answer 1

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

Explanation:

We need to find the derivative with respect to `x`, `dy//dx`.

When we differentiate `y`, since it's a function that's not `x`, the chain rule will kick in and a `dy//dx` term will arise thanks to the chain rule.

Also don't forget that differentiating `xy` will use the product rule.

Differentiating:

`d/dx(x^3-xy+y^3)=d/dx(1)`

`3x^2-(d/dxx)y-x(d/dxy)+3y^2(d/dxy)=0`

`3x^2-y-xdy/dx+3y^2dy/dx=0`

Solve for `dy/dx`:

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

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