If sin (xy) = x, then find dy/dx

Let u = xy

now dy/dx (sin (u))

= cos (u)

=cos (dy/dx (xy))

= cos (xy) y

We are given the expression sin (xy) = x and is asked for the dy/dx. we can use implicit differentiation to differentiate the function. sin (xy) = xcos (xy) * (x dy + y dx) = dxdx (cos (xy) * y - 1) = - x * cos (xy) dydy/dx = - (cos (xy) * y - 1) / x * cos (xy) dy/dx = - 1/x + 1/x cos (xy)