Question

How do you implicitly differentiate `-1=y^3x-xy-9x^4y`?

Answer 1

You can do it like this:

Explanation:

`-1=y^3x-xy-9x^4`

`D(-1)=D(y^3x-xy-9x^4y)`

`0=y^3cancel(d(x))/(cancel(dx))+x.3y^2.y'-(xy'+ycancel(d(x))/(cancel(dx)))-9(x^4y'+y.36x^3)`

`0=y^3+x.3y^2.y'-xy'-y-9x^4y'-9y.36x^3`

`:.0=y^3+y'(x3y^2-x-9x^4)-9y.36x^3`

`:.y'=((324x^3-y^3))/(x(3y^2-1-9x^3))`