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B
6t(t2+2)2
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C
4t(t2+2)2
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D
5t(t2+2)2
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Solution
The correct option is A8t(t2+2)2 We apply the Quotient Rule with u=t2−2 and v=t2+2 d(uv)dt=(v(dudt)−u(dvdt))v2 dydt=((t2+2).2t−(t2−2).2t)(t2+2)2 dydt=(2t3+4t−2t3+4t)(t2+2)2 dydt=8t(t2+2)2