Implicit dfferentation?

Question

Please explain how to solve this question 
d/dx[sin(x+cosy) ]

Answer 1

d/dx[sin(x+cosy)]

= cos(x+cosy) d/dx (x+cosy)

= cos(x+cosy) [ (dx/dx)+d/dx(cosy) ]

= cos(x+cosy)(1 - siny dy/dx)

Substitute : y' = dy/dx

= cos(x+cosy)(1 - y'siny)

= (1 - y'siny) cos(x+cosy)

Solution :  d/dx[sin(x+cosy)] = (1 - y'siny) cos(x+cosy)