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

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

A

`y[x^(x)(log ex)log x+x^(x)]`

B

`y[x^(x)(log ex)log x+x]`

C

`y[x^(x)(log ex)log x+x^(-1)]`

D

`y[x^(x)(log_(e)x)log x+x^(-1)]`

Text Solution

Verified by Experts

`y=""_(x)(x^(x))`
`"or "log y= x^(x) log x`
`"or "(1)/(y)(dy)/(dx)=(dz)/(dx)log x +(1)/(x)z("where "x^(x)=z)`
`"or "(dy)/(dx)=x^((x^(x)))[x^(x)(log ex)log x + x^(x-1)]" "(because(dz)/(dx)=x^(x) log ex)`
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