d dx _7 ( _7 x)= - Vidyadip

MCQ

${d \over {dx}}{\log _7}({\log _7}x)=$

A
${1 \over {x{{\log }_e}x}}$
B
${{{{\log }_e}7} \over {x{{\log }_e}x}}$
✓
${{{{\log }_7}e} \over {x{{\log }_e}x}}$
D
${{{{\log }_7}e} \over {x{{\log }_7}x}}$

✓

Answer

Correct option: C.

${{{{\log }_7}e} \over {x{{\log }_e}x}}$

c
(c) $\frac{d}{{dx}}[{\log _7}({\log _7}x)] = \frac{d}{{dx}}\left( {\frac{{{{\log }_e}({{\log }_7}x)}}{{{{\log }_e}7}}} \right)$

${1 \over {x{{\log }_e}x}} \cdot \frac{1}{{{\log }_{e}}7}$ = $\frac{{{\log }_{7}}e}{x{{\log }_{ex}}}$

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