Limits Continuity And Differentiability Question 53
Question: If $ s=\sqrt{t^{2}+1} $ , then $ \frac{d^{2}s}{dt^{2}} $ is equal to
Options:
A) $ \frac{1}{s} $
B) $ \frac{1}{s^{2}} $
C) $ \frac{1}{s^{3}} $
D) $ \frac{1}{s^{4}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ s=\sqrt{t^{2}+1} $
$ \Rightarrow \frac{ds}{dt}=\frac{t}{\sqrt{t^{2}+1}}\Rightarrow \frac{d^{2}s}{dt^{2}}=\frac{1}{\sqrt{{{( t^{2}+1 )}^{3}}}} $
$ \Rightarrow \frac{d^{2}s}{dt^{2}}=\frac{1}{s^{3}} $
BETA
