Question

What is the implicit derivative of `1= xysin(xy)`?

Answer 1

`(dy)/(dx)=-y/x`

Explanation:

We canwrite `1=xysin(xy)` as

`xy=csc(xy)`

Hence implict derivative is given by

`y+x(dy)/(dx)=-csc(xy)cot(xy)(y+x(dy)/(dx))`

or `(dy)/(dx)(x(1+csc(xy)cot(xy))=-y(1+csc(xy)cot(xy))`

or `(dy)/(dx)=-y/x`