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Mathematics
The derivatives of (log x )xwith respect to log x is
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Q. The derivatives of $(log x )^x$with respect to log x is
A
$(log\,x)^x\left[\frac{1}{log\,x}+log(log\,x)\right]$
B
$(log\,x)^x\left[{log\,x}+\frac{1}{log(log\,x)}\right]$
C
$x(log\,x)^x\left[\frac{1}{log\,x}+ log\,(log\,x)\right]$
D
None of the above.
Solution:
Correct answer is (c) $x(log\,x)^x\left[\frac{1}{log\,x}+ log\,(log\,x)\right]$