## Answers

#### Explanation:

# -y = x^3y^2 - 3x^2y^2 + xy^4 #

We differentiate everything wrt

# -d/dx(y) = d/dx(x^3y^2) - d/dx(3x^2y^2) + d/dx(xy^4) #

We can just deal with the first term;

# -dy/dx = d/dx(x^3y^2) - d/dx(3x^2y^2) + d/dx(xy^4) #

For the other term we apply the product rule;

# -dy/dx = {(x^3)(d/dxy^2) + (d/dxx^3)(y^2)} - {(3x^2)(d/dxy^2) + (d/dx3x^2)(y^2)} + {(x)(d/dxy^4) + (d/dxx)(y^4)} #

Next we use the chain rule so that we can differentiate wrt

And now we can differentiate the

Finally, we can tidy up, collect terms and factorise

Dy/dx + 2x^3ydy/dx - 6x^2ydy/dx + 4xy^3dy/dx = 6xy^2 -y^4 - 3x^2y^2 #