Question

use implicit differentiation to find dy/dx for the curve defined by sin(xy^2)=y+3x

Answer 1

implicit is all about using differentials. whenever u differntiate with respect to x, attatch a dx/dx, which is always 1. Whenever u dif with respect to y, attatck a dy/dx. Differentiiate everything and solve for dy dx. SO:

cos(xy^2)(2(y+x dy/dx) = dy/dx +3
)

Answer 2

now solve for dydx

Answer 3

okay I got dy/dx=(3-y^2)/(cosx(xy^2)2y-1, is this correct?