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The derivative of (log x) ^(x) w.r.t x i...

The derivative of `(log x) ^(x) w.r.t x is (log x)^(x-1) [1+ log x log (log x)]`
`R : (d)/(dx) {f (x) ^(g(x))[g (x) (f'(x))/(f (x)) + g'(x) log (f(x) ]`

A

Both A and R are true R is correct reason of A

B

Both A and R are treu R is not correct reason of A

C

A is true but R is false

D

A is false but R is true

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The derivative of (log x ) ^(4) w.r.t x is

    A
    `(log x) ^(x-1) [1+ log x log (log x)]`
    B
    `(log x) ^(x)-1 [1- log x log (log x)]`
    C
    `- (,og x ) ^(x-1)[1- log x log (log x)]`
    D
    `-(log x )^(x-1) [1- log x log (log x)]`

  • The derivative of log _(x )a w.r.t x is

    A
    `(log a)/(x (log x )^(2))`
    B
    `(-(log a ))/(x (log x )^(2))`
    C
    `(log a)/(x (log x ))`
    D
    none

  • The derivative of x ^(log x) w.r.t x is

    A
    `log x.x^((log x) +1)`
    B
    `log x.x^((log x) -1)`
    C
    `2log x.x^((log x) +1)`
    D
    `2log x.x^((log x) -1)`

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