If `sin^2x+cos^2y=1` find `(dy)/(dx)`

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

If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

If y=cos^2x , then find (dy)/(dx) .

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

If x=a(2theta-sin2theta) and y=a(1-cos2theta) find (dy)/(dx) when theta = pi/3

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

If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2) ,x is [-1/2,0] , find (dy)/(dx)

x=a cos t, y=b sin t find 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 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 .