`e^-y=1`, find `dy/dx`

4.If y = e^(-x^2), find dy/dx

If y=e^-x , find dy/dx.

y=1/(1+x) find dy/dx

If x y=e^(x-y) , find (dy)/(dx) .

If y=x e^x , find dy/dx

If y=(sinx)/(e^x) , find (dy)/(dx)

If y=x^x , find (dy)/(dx) at x=e .

If (tan^(-1)x)^(y)+y^(cotx)=1, then find (dy)/(dx).

If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) and (dx)/(dy) . Also, show that (dy)/(dx)dot(dx)/(dy)=1 .

y=e^(x) find (dy)/(dx)