If y = _2 [ _2 (x)], then dy dx is equal to - Vidyadip

MCQ

If $y = {\log _2}[{\log _2}(x)]$, then ${{dy} \over {dx}}$ is equal to

✓
${{{{\log }_2}e} \over {x{{\log }_e}x}}$
B
${1 \over {{{\log }_e}x{{\log }_e}2}}$
C
${1 \over {{{\log }_e}{{(2x)}^x}}}$
D
None of these

✓

Answer

Correct option: A.

${{{{\log }_2}e} \over {x{{\log }_e}x}}$

a
(a) $y = {\log _2}[{\log _2}(x)] = {\log _e}({\log _e}x.{\log _2}e).{\log _2}e$

$ = [{\log _e}{\log _e}x + {\log _e}({\log _2}e)]{\log _2}e$

$\therefore \frac{{dy}}{{dx}} = {\log _2}e.\frac{1}{{x{{\log }_e}x}}$.

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