Question

How do you implicitly differentiate `y= xy^2 + y^2 e^(xy)`?

Answer 1

`dy/dx=(y^2+y^3e^(xy))/(1-2xy -2ye^(xy) -xy^2e^(xy))`

Explanation:

`y=xy^2+y^2e^(xy)`

`dy/dx=y^2+2xy dy/dx+y^3e^(xy)+2ye^(xy) dy/dx+xy^2e^(xy)dy/dx`

`dy/dx-2xy dy/dx-2ye^(xy) dy/dx-xy^2e^(xy)dy/dx=y^2+y^3e^(xy)`

`dy/dx(1-2xy -2ye^(xy) -xy^2e^(xy))=y^2+y^3e^(xy)`

`dy/dx=(y^2+y^3e^(xy))/(1-2xy -2ye^(xy) -xy^2e^(xy))`