A) \[-\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}\]
B) \[\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}\]
C) \[-\frac{1}{{{(t+1)}^{2}}}-\frac{1}{{{(t+2)}^{2}}}\]
D) None of the above
Correct Answer: A
Solution :
\[y=\frac{1}{(t+2)(t+1)}\] \[y=-\frac{1}{t+2}+\frac{1}{t+1}\] On differentiating w.r.t.\[t,\] \[\Rightarrow \] \[\frac{dy}{dt}=\frac{1}{{{(t+2)}^{2}}}-\frac{1}{{{(t+1)}^{2}}}\]
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