Firstly multiply everything by " "(y-x)" " (y−x) to remove the award denominator.
assuming y!=xy≠x
4(y-x)=y(y-x)-e^(2y)4(y−x)=y(y−x)−e2y
4y-4x=y^2-xy-e^(2y)4y−4x=y2−xy−e2y
now differentiate.
d/(dx)(4y-4x)=d/(dx)(y^2-xy-e^(2y))ddx(4y−4x)=ddx(y2−xy−e2y)
4(dy)/(dx)-4=2y(dy)/(dx)-(y+x(dy)/(dx))-2(dy)/(dx)e^(2y)4dydx−4=2ydydx−(y+xdydx)−2dydxe2y
now rearrange.
4(dy)/(dx)-2y(dy)/(dx)+x(dy)/(dx)+2(dy)/(dx)e^(2y)=4-y4dydx−2ydydx+xdydx+2dydxe2y=4−y
(dy)/(dx)[4-2y+x+2e^(2y)]=4-ydydx[4−2y+x+2e2y]=4−y
(dy)/(dx)=(4-y)/[4-2y+x+2e^(2ydydx=4−y4−2y+x+2e2y
