If log[log{log(x)}] = y, find \(\rm \frac{{dy}}{{dx}}\)
1
\(\rm \frac{{dy}}{{dx}}{\rm{\;}} = \left( {\frac{1}{{\left[ {\left( {logx} \right)\log \left\{ {\log \left( x \right)} \right\}} \right]}}} \right)\)
2
\(\rm \frac{{dy}}{{dx}}{\rm{\;}} = \left( {\frac{1}{{\left[ {\left( x \right)\left( {logx} \right)\log \left\{ {\log \left( x \right)} \right\}} \right]}}} \right)\)
3
\(\rm \frac{{dy}}{{dx}}{\rm{\;}} = \left( {\frac{1}{{\left[ {x\log \left\{ {\log \left( x \right)} \right\}} \right]}}} \right)\)
4
None of these