what is dy/dx of x^2 + sin(xy) +y^2 = 0?
I would guess the answer is
2x + cos (xy)* y = 0
Is this correct?
However yes, the derivative of sin(u) with respect to x is cos(u)(du/dx). And the derivative of u= xy, with respect to x, is (dx/dx)y+ x(dy/dx)= y+ xdy/dx so that the derivative of sin(xy), with respect to x, is cos(xy)(y+ x dy/dx).