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=2x^(n+1)+3xn ,then x^2d^2y/dx^2 is

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 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 !)

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

If y^2=a x^2+b x+c ,then y^3(d^2y)/(dx^2) is (a)a constant (b)a function of x only (c)a function of y only (d)a function of xa n dy

If a x^2+2h x y+b y^2=1,t h e n(d^2y)/(dx^2) is (a) (h^2-a b)/((h x+b y)^2) (b) (a b-h^2)/((h x+b y)^2) (h^2+a b)/((h x+b y)^2) (d) none of these

If y= Ae^(mx) +Be^(nx) , show that (d^(2)y)/(dx^(2))-(m+n)(dy)/(dx)+mny=0 .

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 y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a) y/x(1n x^(oox-1))+21 nx1n(1nx)) (b) y/x(logx)^("log"(logx))(2log(logx)+1) (c) y/(x1nx)[(1nx)^2+21 n(1nx)] (d) y/x(logy)/(logx)[2log(logx)+1]