If y and x are both functions of a variable t then dy/dx is (dy/dt) / (dx/dt): that is, it is the quotient of the two derivatives. In this case x = sin t and y = sec t, so dx/dt is cos t and y is 1/cos t, so dy/dt is sin t/cos^2 t (by the chain rule). So dy/dx is sin t/cos^3 t.