Question

How do you differentiate `cos(x/y) = x/y`?

Answer 1

`(dy)/(dx) = 1/t_1` where `t_1` is the unique root of `cos(t)=t`

Explanation:

The equation `cos(t) = t` has only one solution, `t_1 ~~ 0.7390851332`

So our original equation amounts to `x/y = t_1`

Hence `y = x/t_1`

So `(dy)/(dx) = 1/t_1 ~~ 1.353024`

graph{(y-cos(x))(y-x)=0 [-4.44, 5.56, -2.03, 2.97]}