its difficulty problem.

Question

find dy/dx by implicit differentiation
1.4 cos x sin y = 1

2.tan(x/y)= x+y

Answer 1

1.) 4 cos x sin y = 1
2.) tan(x/y)= x+y

Answer 2

using product rule and chain rule,

4 (-sinx)(siny) + 4(cosx)(cosy y') = 0
y' = sinx*siny / cosx*cosy
= tanx * tany
--------------------
sec^2(x/y)*(1/y - x/y^2 * y') = 1 + y'

y*sec^2(x/y) - y^2
--------------------- = y'
y^2 + x*sec^2(x/y)