Question

if x^2 + y^3 = (x^3)(y^2) then dy/dx = ? thanks

Answer 1

x^2 + y^3 = (x^3)(y^2)
differentiate with respect to x

2x +3y²(dy/dx) = 3x²y²+x&sup3*2y*(dy/dx)

Group dy/dx on left:
(dy/dx)(3y²-2x³y)=3x²y²-2x
dy/dx=(3x²y²-2x)/(3y²-2x³y)

check my work.

Answer 2

implicit differentiation y^5 + x^2y^3=1 + x^4y