Calculus
posted by angie .
find y' if sin^1(xy)=cosy

Use implicit differentiation:
sin^1(xy)=cosy
sin(cos(y))=xy
differentiate both sides with respect to x
(use chain rule):
cos(cos(y))(sin(y))y'=y+xy'
Collect terms and solve for y'
y'=y/(cos(cos(y))sin(y)+x)