X

3

y-2x

2

+y

4

=8

Find / dfrac{dy}{dx}

dx

dy

.

x^3y-2x^2+y^4=8

take the derivative of each part, using the product rule on the first term

x^3 dy + y*3x^2dx - 4xdx+4y^3 dy = 0

gather the dy and dx terms together

dy (x^3+4y^3) - dx (-3x^2y+4x) = 0

dy terms on the left, dx terms on the right

dy (x^3+4y^3) = dx (-3x^2y+4x)

dy divided by dx

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

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