Find dy/dx cot xy+2=y

Question

not coming out right..........

Answer 1

We differentiate implicitly this equation: d/dx(cotxy+ 2) = dy/dx; - csc²xy(y + xdy/dx) = dy/dx;

-ycsc²xy = (1 + xcsc²xy)dy/dx; dy/dx = - ycsc²xy/(1 + xcsc²xy)