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

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

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) (x(dy)/(dx)-y) ^2 (b) x (dy/dx)-y (c) y(dy/dx)-x (d) (y(dy/dx)-x)^2

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

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

Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx)i se q u a lto (tant)/(2t) (b) (tant)/(t^2) (c) tan t/(2t^2) (d) (t a tt^2)/(2t^2)

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=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (a) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^2) (b) (varphi^(prime)psi^('')-psi'varphi' ')/((varphi^(prime))^3) (c) varphi^('')/psi^('') (d) psi^('')/varphi^('')

If y^3-y=2x ,t h e n(x^2-1/(27))(d^2y)/(dx^2)+x(dy)/d= y b. y/3 c. y/9 d. y/(27)

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot