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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
${{{d^2}x} \over {d{y^2}}}$=
  • A
    ${1 \over {{{(dy/dx)}^2}}}$
  • B
    ${{\left( {{d^2}y/d{x^2}} \right)} \over {{{\left( {dy/dx} \right)}^2}}}$
  • C
    ${{{d^2}y} \over {d{x^2}}}$
  • ✓
    ${{\left( { - {d^2}y/d{x^2}} \right)} \over {{{\left( {dy/dx} \right)}^2}}}$
✓

Answer

Correct option: D.
${{\left( { - {d^2}y/d{x^2}} \right)} \over {{{\left( {dy/dx} \right)}^2}}}$
d
(d) $\frac{{{d^2}x}}{{d{y^2}}} = \frac{d}{{dy}}\,\left( {\frac{{dx}}{{dy}}} \right) = \frac{d}{{dy}}\left( {\frac{1}{{\frac{{dy}}{{dx}}}}} \right) = \frac{{ - 1}}{{{{\left( {\frac{{dy}}{{dx}}} \right)}^2}}}\,.\,\frac{{{d^2}y}}{{d{x^2}}}$.

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