Question

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

Answer 1

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) 

Answer 2

Let u = xy
now dy/dx(sin(u))
= cos(u)
=cos(dy/dx(xy))
= cos(xy)y