Question

How do you differentiate `x^4(x+y)=y^2(3x-y)`?

Answer 1

`dy/dx=(3y^2-5x^4-4x^3y)/(x^4 -6xy+3y^2)`

Explanation:

This can be by implicit differentiation. Rewrite it as `x^5+x^4 y= 3xy^2 - y^3`. Now differentiate term wise, `5x^4 +x^4 dy/dx + 4x^3 y= 3y^2+6xydy/dx-3y^2 dy/dx`

`(x^4 -6xy+3y^2)dy/dx=3y^2-5x^4-4x^3y`

`dy/dx=(3y^2-5x^4-4x^3y)/(x^4 -6xy+3y^2)`