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 y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)-y+(x^n)/(n !)=0.

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

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 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

(d^n)/(dx^n)(logx)= (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

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

If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is equal to

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))