equals

Engineering

Mathematics

Successive Differentiation

Question

$\frac{d^{2} x}{{dy}^{2}}$ equals

$\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right){\left( {\frac{{dy}}{{dx}}} \right)^{ - 2}}$

$ - {\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{ - 1}}{\left( {\frac{{dy}}{{dx}}} \right)^{ - 3}}$

${\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{ - 1}}$

$ - \left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)\,{\left( {\frac{{dy}}{{dx}}} \right)^{ - 3}}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$\frac{{dy}}{{dx}} = \frac{1}{{\frac{{dx}}{{dy}}}}$

$\frac{{{d^2}y}}{{d{x^2}}} = \frac{d}{{dx}}\left( {\frac{1}{{dx/dy}}} \right) = \frac{d}{{dy}}\left( {\frac{1}{{dx/dy}}} \right)\frac{{dy}}{{dx}} = - \frac{1}{{{{\left( {\frac{{dx}}{{dy}}} \right)}^2}}}.\frac{{\frac{{{d^2}x}}{{d{y^2}}}}}{{\frac{{dx}}{{dy}}}} = \frac{{ - \frac{{{d^2}x}}{{d{y^2}}}}}{{{{\left( {\frac{{dx}}{{dy}}} \right)}^3}}}$