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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = {\log _{10}}{x^2}$, then ${{dy} \over {dx}}$ is equal to
  • A
    ${2 \over x}$
  • ✓
    ${2 \over {x{{\log }_e}10}}$
  • C
    ${1 \over {x{{\log }_e}10}}$
  • D
    ${1 \over {10x}}$
✓

Answer

Correct option: B.
${2 \over {x{{\log }_e}10}}$
b
(b) Given $y = {\log _{10}}{x^2}$

$y = \frac{{{{\log }_e}{x^2}}}{{{{\log }_e}10}}$,      $\left( \because {{\log }_{a}}b=\frac{{{\log }_{e}}b}{{{\log }_{e}}a} \right)$

$y = \frac{{2{{\log }_e}x}}{{{{\log }_e}10}}$,

$\therefore \frac{{dy}}{{dx}} = \frac{2}{{x{{\log }_e}10}}$.

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