why can't 4sinx / 15cos3y turn into (4/15)tan(x/3y)

Question

original problem is find dy/dx of 4cosx+5sin3y=13

Answer 1

It looks like you are assuming that sinx/cos3y = tan(x/3y), but that is not correct.

 

tan(x/3y) = sin(x/3y) / cos(x/3y), 

 

which is not the same as sinx/cos3y.