If \[f(x)={{\cos }^{-1}}\left[ \frac{1-{{(\log x)}^{2}}}{1+{{(\log x)}^{2}}} \right]\,,\]then the value of \[f'(e)=\] [Karnataka CET 1999; Pb. CET 2000]

If \[f(x)={{\cos }^{-1}}\left[ \frac{1-{{(\log x)}^{2}}}{1+{{(\log x)}

1.	If \[f(x)={{\cos }^{-1}}\left[ \frac{1-{{(\log x)}^{2}}}{1+{{(\log x)}^{2}}} \right]\,,\]then the value of \[f'(e)=\] [Karnataka CET 1999; Pb. CET 2000]
A.	1
B.	1/e
C.	2/e
D.	\[\frac{2}{{{e}^{2}}}\]
Answer» C. 2/e

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If \[f(x)={{\cos }^{-1}}\left[ \frac{1-{{(\log x)}^{2}}}{1+{{(\log x)}^{2}}} \right]\,,\]then the value of \[f'(e)=\] [Karnataka CET 1999; Pb. CET 2000]

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