Find the dy/dx , x^2+y^2=sin(xy)   

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to use implicit differentiation and chain rule such that:

`2x + 2y(dy)/(dx) = cos(xy)*(y + x*(dy)/(dx))`

You need to open the brackets such that:

`2x + 2y(dy)/(dx) = y*cos(xy) + x*cos(xy)*(dy)/(dx)`

You need to isolate the terms containing`(dy)/(dx)`  to the left such that:

`2y(dy)/(dx) -x*cos(xy)*(dy)/(dx) = y*cos(xy) - 2x`

You need to factor out `(dy)/(dx)`  such that:

`(dy)/(dx)*(2y - x*cos(xy)) = y*cos(xy) - 2x`

`(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy))`

Hence, evaluating `(dy)/(dx)`  yields `(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy)).`