please explain how to use implicit differentiation to obtain: `dy/dx` `[x^2y+5xy^3-x=2]`
The given equation is: `x^2y+5xy^3-x=2`
y is not an explicit function of x, hence in order to find `dy/dx` , recourse of implicit differentiation has to be resorted to.
Differentiate both sides of the equation with respect to x, getting
Use the product rule twice, and note that `d/dx(phi(y))=d/dy(phi(y)) * dy/dx`