Let `y^(')(x)+y(x)g^(')(x)=g(x)g^(')(x),y(0)=0, x in R`, where `f^(')(x)` denotes `(df(x))/(dx)`, and `g(x)` is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of `y(2)` is ……………………

Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , where f^(prime)(x) denotes (dy(x))/(dx), and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of y(2) is______

Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , where f^(prime)(x) denotes (dy(x))/(dx), and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of y(2) is______

Let x=f(t) and y=g(t), where x and y are twice differentiable function. If f'(0)= g'(0) =f''(0) = 2. g''(0) = 6, then the value of ((d^(2)y)/(dx^(2)))_(t=0) is equal to

Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continuous then f'(x) is

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

let f(x) = { g(x).cos(1/x) if x!= 0 and 0 if x= 0 , where g(x) is an even function differentiable at x= 0 passing through the origin then f'(0)

Let f (x), g(x) be two real valued functions then the function h(x) =2 max {f(x)-g(x), 0} is equal to :

Let f(x+y) = f(x) f(y) and f(x) = 1 + x g(x) G(x) where lim_(x->0) g(x) =a and lim_(x->o) G(x) = b. Then f'(x) is

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)4f(x_0),g^(prime)(x_0)=-7g(x_0), then the value of g^(prime)(1) is ________