`(x^3)(y^3) - y = x` Find `dy/dx` by implicit differentiation.

Textbook Question

Chapter 2, 2.5 - Problem 7 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`(x^3)(y^3)-y=x`

Differentiating both sides with respect to x,

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

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

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

`3x^3y^2dy/dx+3x^2y^3-dy/dx=1`

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

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

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

We’ve answered 318,917 questions. We can answer yours, too.

Ask a question