Question

How would you find the derivative of this implicit function?

1+x=sin(xy^2)

Answer 1

Use Chain Rule
1=cos(xy^2)(y^2+2xyy')
1=cos(xy^2)y^2+(2xy)cos(xy^2)(y')
[1-cos(xy^2)y^2]/[(2xy)cos(xy^2)]=y'