Implicit differentiation to find dy/dx in terms of x and y of

Question

x^3(y)-y^3(x)=x?

Answer 1

The funtion is x³y - y³x = x .

Differentiate with respect to x .

[x³y' + y(3x²)] - [ y³(1) + x(3y²)y' ] = 1 

x³y' + 3x²y -  y³ - 3xy²y'  = 1 

y'(x³ -3xy² ) + 3x²y -  y³ = 1 

y'(x³ -3xy² ) = 1 - 3x²y +  y³

y' = (1 - 3x²y +  y³)/(x³ -3xy² ) .

So the implicit Differentiation of  x³y - y³x = x is   dy/dx = (1 - 3x²y +  y³)/(x³ -3xy² ) .