MCQ
$\frac{d}{{dx}}\left( {{{\log }_{{a^n}}}\ {x^n}} \right) = .........$
- A$\frac{1}{x}{\log _e}a$
- ✓$\frac{1}{{x{{\log }_e}a}}$
- C$\frac{1}{x}{\log _a}e$
- D$xlog_e \ a$
$\frac{d}{{dx}}\left[ {{{\log }_{{a^n}}}{x^n}} \right] = \frac{d}{{dx}}\left[ {\frac{n}{n}{{\log }_a}x} \right]$
$ = \frac{d}{{dx}}\left[ {\frac{{{{\log }_e}x}}{{{{\log }_e}a}}} \right]$
$ = \frac{1}{{x{{\log }_e}a}}$
$ = \frac{1}{x}{\log _a}e$
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$f\left( x \right) = \int_1^x {\left\{ {2\left( {t - 1} \right){{\left( {t - 2} \right)}^3} + 3{{\left( {t - 1} \right)}^2}{{\left( {t - 2} \right)}^2}} \right\}} dt$ એ $x$ ની કઇ કિમત આગળ મહત્તમ થાય ?
$(S1)$ $A ^{13} B ^{26}- B ^{26} A ^{13}$ સંમિત છે.
$(S2)$ $A ^{26} C ^{13}- C ^{13} A ^{26}$ સંમિત છે.
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