Questions & Answers

Question

Answers

Answer
Verified

Consider the given differentiation

\[y = {\sin ^2}\left( {{x^2}} \right)\]

Differentiate with respect to \[{x^2}\]

\[\dfrac{{dy}}{{d{x^2}}} = \dfrac{{d{{\sin }^2}{x^2}}}{{d{x^2}}}\]

\[\dfrac{{dy}}{{d{x^2}}} = 2\sin {x^2}\cos {x^2}\]

As we know that \[2{\text{ }}sin{\text{ }}xcos{\text{ }}x = sin{\text{ }}2x{\text{ }}so,\]

\[2\sin {x^2}\cos {x^2} = \sin 2{x^2}\]

\[\dfrac{{dy}}{{d{x^2}}} = \sin \left( {2{x^2}} \right)\]

Hence, this is the answer

\[\dfrac{{df}}{{dg}} = \dfrac{{df}}{{db}} \times \dfrac{{db}}{{dg}} = \dfrac{{df/db}}{{db/dg}}\]