`sin^2y+cosxy=k` find `(dy)/(dx)`

If y=x^(sin x), then find (dy)/(dx)

If y=(sin x)^(x)+x^(2) find (dy)/(dx)

If (cos"x")^y=(sin y)^x , find (dy)/(dx)

If y^(x)=x^(sin y) find (dy)/(dx)

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

If y = e^( sin x^3) , 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 .

If y=x^(sin^(-1)x) then finde (dy)/(dx) .

If y =sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).

If y sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).