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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = a{x^{n + 1}} + b{x^{ - n}}$, then ${x^2}{{{d^2}y} \over {d{x^2}}} = $
  • A
    $n\,(n - 1)y$
  • ✓
    $n\,(n + 1)y$
  • C
    $ny$
  • D
    ${n^2}y$
✓

Answer

Correct option: B.
$n\,(n + 1)y$
b
(b) $y = a{x^{n + 1}} + b{x^{ - n}} $

$\Rightarrow \frac{{dy}}{{dx}} = (n + 1)a{x^n} - nb{x^{ - n - 1}}$

==> $\frac{{{d^2}y}}{{d{x^2}}} = n(n + 1)a{x^{n - 1}} + n(n + 1)b{x^{ - n - 2}}$

==> ${x^2}\frac{{{d^2}y}}{{d{x^2}}} = n(n + 1)y$.

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