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\\ (\partial f)/(\partial x) =7*(sin(\pi*x)+cos(\pi*y))^6*cos(\pi*x)*\pi\\ (\partial f)/(\partial y) =7*(sin(\pi*x)+cos(\pi*y))^6 * (-sin(\pi*y ))*\pi\\ (dy)/(dx) =-((\partial f)/(\partial x))/( (\partial f)/(\partial y))\\\\ =-(7*(sin(\pi*x)+cos(\pi*y))^6* cos(\pi*x)*\pi)/(7*(sin(\pi*x)+cos(\pi*y))^6*(-sin(\pi*y))*\pi)\\ =(cos(\pi*x))/(sin(\pi*y))`