X3 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)

a 90 degree rotation across the the origin followed by a reflection across the x-axis.

step-by-step explanation: