If `sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx)` is equal to `x/y` (b) `y/(x^2)` `(x^2-y^2)/(x^2+y^2)` (d) `y/x`

If x y+y^2=tanx+y ,t h e n(dy)/(dx)dot

If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

Solve (dy)/(dx)=((x+y)^2)/((x+2)(y-2))

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

If y= sin^(-1)x , show that (1-x^(2)) (d^(2)y)/(dx^(2))-x(dy)/(dx)0 .

Solve (dy)/(dx)+(y^(2))/(x^(2))=(y)/(x)