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If F(x)=f(x)dotg(x) and f^(prime)(x)dot...

If `F(x)=f(x)dotg(x)` and `f^(prime)(x)dotg^(prime)(x)=c ,` prove that `(F")/F=f^(primeprime)/f+g^(primeprime)/g+(2c)/(fg)&F^(primeprimeprime)/F=f^(primeprimeprime)/f+g^(primeprimeprime)/g`

Answer

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Knowledge Check

  • If F(x)=f(x).g(x) and f'(x).g'(x)=c , then

    A
    `F'=c(f)/(f')+(g)/(g')`
    B
    `F'=c(f)/(f')-(g)/(g')`
    C
    `(F'')/(F)=(f'')/(f)+(g'')/(g)+(2c)/(fg)`
    D
    None of these

  • If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

    A
    4
    B
    `1/4`
    C
    2
    D
    `1/2`

  • If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

    A
    `2x`
    B
    `2.f(x)`
    C
    `[f(x)]^2`
    D
    none of these.

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