MCQ
જો $f\left( x \right) = {\log _7}\left( {{{\log }_3}x} \right),$ તો $f'\left( x \right) = .......$
- A$\frac{1}{{x\log 7\log 3}}$
- B$\frac{1}{{\log 3\log x}}$
- ✓$\frac{1}{{x\log x\log 7}}$
- D$\frac{1}{{x\log x}}$
$f\left( x \right) = {\log _7}\left( {{{\log }_3}x} \right)$
$ = {\log _7}\left( {\frac{{\log x}}{{\log 3}}} \right)$
$ = {\log _7}\left( {\log x} \right) - {\log _7}\left( {\log 3} \right)$
$ = \frac{{\log \left( {\log x} \right)}}{{\log 7}} - {\log _7}\left( {\log 3} \right)$
$\therefore f'\left( x \right) = \frac{1}{{\log 7}}.\frac{1}{{\log x}}.\frac{1}{x} = \frac{1}{{x\log x\log 7}}$
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(જ્યાં $c$ એ સંકલનનો અચળાંક છે.)