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If y=(x^x)^x then (dy)/(dx) is...

If `y=(x^x)^x` then `(dy)/(dx)` is

A

xy(1+ logx)

B

xy(1+ 2 logx)

C

`x/y (1 + log x)`

D

`x/y (1 + 2 log x)`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If y= x^(x^(2x) ) ,then (dy)/(dx) =

    A
    ` x^(x^(2x)) x^(2x) log x( 2+ 2log x +( 1)/(xlog x ))`
    B
    ` x^(x^(2x)) x^(2x) log x( 2+ log x +( 1)/(xlog x ))`
    C
    ` x^(x^(2x)) x^(2x) ( 2+ 2log x +( 1)/(xlog x ))`
    D
    ` x^(x^(2x)) x^(2x) ( 2+ log x +( 1)/(xlog x ))`

  • If y=(x)^(x) + 10^(x) then (dy)/(dx) =?

    A
    `x^(x)(1+ logx) + 10^(x) log 10`
    B
    `x^(x) (1+log x)- 10^(x) log 10`
    C
    `x(1+ log x) + 10^(x) log 10`
    D
    `x^(x)(1+ log x) + 10^(x) log 10`

  • If y=x^(x) +a^(a) ,then (dy)/(dx)=

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

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