Question
find y' if sin^-1(xy)=cosy
Answers
MathMate
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)
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)