Question

Find dy/dx by implicit differentiation. 3+3x=sin(xy^2)

Answer 1

derivative of both sides w/respect to x:
3=cos(xy^2)(y^2+2yxy')
(chain rule and product rule on right side)
y^2+2yxy'=3sec(xy^2)
y'=3[sec(xy^2)-y^2]/2xy