" sin y."(dy)/(dx)+(1)/(x)cos y=x^(4)cos^(2)y

(dy)/(dx)=(x+sin x)/(y+cos y)

(dy)/(dx)=sin(x+y)+cos(x+y)

Find (dy)/(dx) when : (cos x)^(y)=(sin y)^(x)

If sin y=x sin(a+y), then show that: (dy)/(dx)=(sin a)/(1-2x cos a+x^(2))

If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= (a) -y/x (b) (3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y)) (c) (3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y)) (d) (sin^2(a+y))/(sina)

Solve: (i) sin^(-1)((dy)/(dx))=x+y (ii) (dy)/(dx)=cos(x+y) (iii) (dy)/(dx)=(4x+y+1)^2

Solve (dy)/(dx)=sin(x+y)+cos (x+y)

If y = x sin y prove that (dy) / (dx) = (sin y) / ((1-x cos y))

Ify,=sqrt(((1+cos x)/(2))), provethat (dy)/(dx)=-(1)/(2)(sin x)/(2) If y,=sqrt((1+sin x)/(1-sin x)), prove that cos x(dy)/(dx)=y

If sin y = x sin (a + y) prove that (dy) / (dx) = (sin a) / (1-2x cos a + x ^ (2))