Engineering Board Exam Reviewer · Higher-Order Derivatives · medium

Find d2y/dx2 if y= ≤ft(x2+1 ).

1. - 2≤ft(x2 + 1 )2
2. 2 x2 - 2≤ft(x2 + 1 )2
3. 2 xx2 + 1
4. 2 - 2 x2≤ft(x2 + 1 )2

Answer

D. 2 - 2 x2≤ft(x2 + 1 )2

Solution

y'=2x/x2+1. By the quotient rule, y''=2(x2+1)-2x(2x)/(x2+1)2=2-2x2/(x2+1)2.

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