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

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

A

`y x^(y-1)`

B

`(y^(2))/(x(1-y log x))`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given
` y = x^(y)`
Taking log on both sides, we get
log y = y log x
` Rightarrow 1/y .(dy)/(dx) =y .1/x + (dy)/(dx) . Log x`
` Rightarrow (dy)/(dx) [ 1/y - log x] = y/x `
` Rightarrow (dy)/(dx) = (y^(2))/(x(1-y log x))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 01-Paper 2 (Mathematics)
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