A) \[\frac{2{{t}^{2}}+3}{3{{t}^{5/3}}}\]
B) \[\frac{2{{t}^{2}}+3}{{{t}^{5/3}}}\]
C) \[\frac{2(2{{t}^{2}}+3)}{{{t}^{5/3}}}\]
D) \[\frac{2(2{{t}^{2}}+3)}{3{{t}^{5/3}}}\]
Correct Answer: D
Solution :
\[y={{t}^{4/3}}-3{{t}^{-2/3}}\] \[\therefore \frac{dy}{dt}=\frac{4}{3}{{t}^{1/3}}+3\times \frac{2}{3}{{t}^{-5/3}}=\frac{4{{t}^{2}}+6}{3{{t}^{5/3}}}=\frac{2(2{{t}^{2}}+3)}{3{{t}^{5/3}}}\].
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