Let f,g and h be differentiable function. If `f(0)=1,g(0)=2, h(0)=3` and the derivatives of their pair wise products at x = 0 are `(fg)'(0)=6,(gh)'(0)=4 and (hf)'(0)=5` then the value of `((fgh)'(0))//2` is

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) .

Let f,g: (a,b) to R be differentiable functions show that d ((f)/(g)) = (gf' dx - fg'dx)/(g ^(2)) (where g ne 0)

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n dg(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

Let f be differentiable function such that f'(x)=7-3/4(f(x))/x,(xgt0) and f(1)ne4" Then " lim_(xto0^+) xf(1/x)

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let h(x) be differentiable for all x and let f(x) = (kx=e^(x)) h(x) where k is some constant. If h(0)=5, h^(')(0) = -2 and f^(')(0) =18 then the value of k is equal to

Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0),g(0),f(1)=6. Let there exists real number c in (0,1) such taht f^(prime)(c)=2g^(prime)(c)dot Then the value of g(1) must be 1 (b) 3 (c) -2 (d) -1

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