Question

(sin(pi*x)+cos(pi*y))^7=36 find the dy/dx by implicit differentiation

Answer 1

Hello,

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