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If y=log(10)x+log(x)10+log(x)x+log(10)10...

If `y=log_(10)x+log_(x)10+log_(x)x+log_(10)10` then what is `((dy)/(dx))_(x=10)` equal to?

A

`1/(x log_(e)10)-(log_(e)10)/(x(log_(e)x)^(2))`

B

`1/(xlog_(e)10)-1/(xlog_(10)e)`

C

`1/(x log_(e)10)-1/(log_(e)x)^(2)`

D

None of these

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The correct Answer is:
A
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