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

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

A

`(x^(x))^(x)(1+2logx)`

B

`(x^(x))^(x)(1+logx)`

C

`x(x^(x))^(x)(1+2logx)`

D

`x(x^(x))^(x)(1+logx)`

Text Solution

Verified by Experts

The correct Answer is:
C
`y=(x^(x))^(x)implieslog_(e)y=xlog_(e)(x^(x))(x)=x^(2)log_(e)x`
`implies1/y (dy)/(dx)=x+2x log_(e)x`
`:.(dy)/(dx)=x(x^(x))^(x)(1+2log_(e)x)`
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