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Suppose f and g are functions having sec...

Suppose f and g are functions having second derivatives f'' and g'' every where . If f(x) .g(x) = 1 for all x and f' and g' are never zero then `(f''(x))/(f'(x))-(g''(x))/(g'(x))` equals

A

`(-2f'(x))/(f(x))`

B

`(2g'(x))/(g(x))`

C

`-(f'(x))/(f(x))`

D

`(2f'(x))/(f(x))`

Text Solution

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The correct Answer is:
B, D
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Knowledge Check

  • Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

    A
    `f(g(x)) gt f(g(x-1))`
    B
    `f(g(x)) gt f(g(x+1))`
    C
    `g(f(x)) gt g(f(x+1))`
    D
    `g(f(x)) gt g(f(x+1))`

  • If f^(1)(x) =g(x) and g^(1)(x) =-f (x) for all x and f(2) = 4 =f^(1) (2) then f^(2) (4) +g^(2)(4) is

    A
    32
    B
    24
    C
    64
    D
    48

  • phi(x) = f(x)g(x) and f'(x)g'(x) = k , then (2k)/(f(x)g(x)) =

    A
    `(phi''(x))/(phi(x)) - (f''(x))/(f(x)) - (g''(x))/(g(x))`
    B
    `(phi''(x))/(phi(x)) + (f''(x))/(f(x)) + (g''(x))/(g(x))`
    C
    `(phi''(x))/(phi(x)) + (f''(x))/(f(x)) - (g''(x))/(g(x))`
    D
    `(phi''(x))/(phi(x)) - (f''(x))/(f(x)) + (g''(x))/(g(x))`

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