Hello,
[tex]f(x,y)=(sin(\pi*x)+cos(\pi*y))^7 -36\\
\dfrac{\partial f}{\partial x} =7*(sin(\pi*x)+cos(\pi*y))^6*cos(\pi*x)*\pi\\
\dfrac{\partial f}{\partial y} =7*(sin(\pi*x)+cos(\pi*y))^6 * (-sin(\pi*y ))*\pi\\
\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f}{\partial x}}{ \dfrac{\partial f}{\partial y}}\\\\
=-\dfrac{7*(sin(\pi*x)+cos(\pi*y))^6* cos(\pi*x)*\pi}{7*(sin(\pi*x)+cos(\pi*y))^6*(-sin(\pi*y))*\pi}\\
=\dfrac{cos(\pi*x)}{sin(\pi*y)}
[/tex]
