Let `f, g and h` are differentiable functions. If `f(0) = 1; g(0) = 2; h(0) = 3` and the derivatives of theirpair wise products at `x=0` are `(fg)'(0)=6;(g h)' (0) = 4 and (h f)' (0)=5` then compute the value of `(fgh)'(0)`.

If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(0)=2,g(0) = 0,f(1)=6,g(1)=2 , then in the interval (0,1)

Given that f(x) = xg (x)//|x| g(0) = g'(0)=0 and f(x) is continuous at x=0 then the value of f'(0)

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

If f(x) and g(x) are differentiable function for 0 le x le 23 such that f(0) =2, g(0) =0 ,f(23) =22 g (23) =10. Then show that f'(x)=2g'(x) for at least one x in the interval (0,23)

Two functions f & g have first & second derivatives at x=0 & satisfy the relations, f(0) = 2/(g(0)), f'(0)=2g'(0) = 4g(0), g"(0)= 5 f"(0)=6f(0) = 3 then-

Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) = If g(x)=(f(2f^(2)(x)+2))^(2), then g'(0) equals

If both f(x) & g(x) are differentiable functions at x=x_0 then the function defiend as h(x) =Maximum {f(x), g(x)}

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

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):