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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}\left( {{x^3}{{\tan }^2}{x \over 2}} \right)=$
  • A
    ${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3x{\tan ^2}{x \over 2}$
  • ✓
    ${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$
  • C
    ${x^3}{\tan ^2}{x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$
  • D
    None of these
✓

Answer

Correct option: B.
${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$
b
(b) $\frac{d}{{dx}}\left( {{x^3}{{\tan }^2}\frac{x}{2}} \right) = 3{x^2}{\tan ^2}\frac{x}{2} + 2{x^3}\tan \frac{x}{2}{\sec ^2}\frac{x}{2}.\frac{1}{2}$

$ = {x^3}\tan \frac{x}{2}{\sec ^2}\frac{x}{2} + 3{x^2}{\tan ^2}\frac{x}{2}$.

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