`(x^2)y + (y^2)x = -2` Find `dy/dx` by implicit differentiation.
1 Answer
gsarora17 | (Level 2) Associate Educator
`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)`