`(x^2)y + (y^2)x = -2` Find `dy/dx` by implicit differentiation.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`x^2y+y^2x=-2`

Differentiating both sides with respect to x,

`x^2d/dx(y)+yd/dx(x^2)+y^2d/dx(x)+xd/dx(y^2)=0`

`x^2dy/dx+y(2x)+y^2+x(2y)dy/dx=0`

`x^2dy/dx+2xydy/dx+2xy+y^2=0`

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

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

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial