Find *dy*/*dx* by implicit differentiation.

x^6(x + y) = y^2(4x − y)

### 1 Answer | Add Yours

Think that y is a function of x and differentiate with respect to the variable x using usual differentiation rules.

`6x^5(x+y)+x^6(1+y')=2y'y(4x-y)+y^2(4-y')`

`7x^6+6x^5y+x^6y'=8y'yx-3y'y^2)+4y^2`

Solve for y':

`y'(x^6-8yx+3y^2)=4y^2-7x^6-6x^5y`

**Solution **`y'=(dy)/(dx)=(4y^2-7x^6-6x^5y)/(x^6-8yx+3y^2)`

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes