Let `y(x,t)={x(t-1);` when `x <= t, t(x-1);` when `t < x and t` is continuous function of x in `[0, 1]`. If `g(x)=int_0^1 f(t)y(x,t)dt` then

Find the derivatives w.r.t. x : x=t log t, y=(log t)/(t)" when " t =1

Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2(t - 1))/(t + 1) - ln t)f(t)dt for t ∈ [1, x] for all x ∈ (1, ∞).Which of the following is true ?

If x = a(t+1/t), y =a(t-1/t), then dy/dx =

Let F(x)=f(x)+f((1)/(x)), where f(x)=int_(t)^(x)(log t)/(1+t)dt (1) (1)/(2)(2)0(3)1(4)2

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

Let g (x,y)=x^2-yx + sin (x+y), x (t) = e^(3t) , y(t) = t^2, t in R. Find (dg)/(dt) .

For x in R, x != 0, if y(x) differential function such that x int_1^x y(t)dt=(x+1)int_1^x t y(t)dt, then y(x) equals:

If x= a(t-1/t), y=a(t+1/t) , then dy/dx =........ A) x/y B) y/x C) -x/y D) -y/x