Answer:
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3).
Step-by-step explanation:
x^5y^2 − x^4y + 2xy^3 = 0
Applying the Product and Chain Rules:
y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0
Separating the terms with derivatives:
y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy = x^4 - 2y*x^5 - 3y^2*2x
dx/dy = (x^4 - 2x^5y - 6xy^2) / (5x^4y^2 - 4x^3y + 2y^3)
Simple. The answer is p=4.5
