Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy

Question

y^2 * x^4 - yx^3 + 2xy^3  =  0

Answer 1

dx / dy  means to find the derivative of x in terms of y.

 

 

y²x⁴ - yx³ + 2xy³ = 0

 

 

Derive both sides of equation using the chain rule.

 

(2yx⁴ + 4y²x³x') - (x³ + 3yx²x') + (2x'y³ + 6xy²) = 0

 

2yx⁴ + 4y²x³x' - x³ - 3yx²x' + 2x'y³ + 6xy² = 0

 

 

Now isolate all the x' terms on one side of the equation.  Move all the other terms to the other side of equation.  Once you do that, factor out a x'.  Then divide both sides of the equation by the coefficient of x'.  And your done.