If `x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2,` then `x^3y (dy)/(dx)=` (a) `0` (b) `1`(c) `-1` (d) non of these

If u=x^2+y^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) 20t^8 (c) 5/(16t^6) (d) non of these

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a n dtany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)) then (dy)/(dx) at t=2 ………….

If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

If x=t^2,y=t^3,t h e n(d^2y)/(dx^2)= (a) 3/2 (b) 3/((4t)) (c) 3/(2(t)) (d) (3t)/2

x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is

x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) -(pi+4)/2 (c) -2 (d) none of these

If x = 3 tant and y = 3 sec t, then the value of (d^2y)/(dx^2)" at" t=pi/4 is

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