A) \[\frac{1}{{{x}^{4}}}\]
B) \[-\frac{t}{{{x}^{2}}}\]
C) \[\frac{1}{x}-\frac{{{t}^{2}}}{{{x}^{3}}}\]
D) \[\frac{1}{x}-\frac{t}{{{x}^{2}}}\]
Correct Answer: C
Solution :
\[{{x}^{2}}={{t}^{2}}+t\] Differentiate wrt x \[2\times \frac{dx}{dt}=2t\] \[v=\frac{dx}{dt}=\frac{t}{x}\] \[a=\frac{dv}{dt}\] \[=\frac{x-t\left( \frac{dx}{dt} \right)}{{{x}^{2}}}\] \[=\frac{x-\left( \frac{{{t}^{2}}}{x} \right)}{{{x}^{2}}}\] \[a=\frac{1}{x}-\frac{{{t}^{2}}}{{{x}^{3}}}\]
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