Engineering Board Exam Reviewer · Derivatives of Algebraic Functions · medium

Find y' if y=≤ft(x+1/x-1 )3.

1. 6 ≤ft(x + 1 )2≤ft(x - 1 )4
2. - 6 ≤ft(x + 1 )2≤ft(x - 1 )4
3. - 3 ≤ft(x + 1 )2≤ft(x - 1 )4
4. 3 ≤ft(x + 1 )2≤ft(x - 1 )2

Answer

B. - 6 ≤ft(x + 1 )2≤ft(x - 1 )4

Solution

Chain rule: y'=3≤ft(x+1/x-1 )2·(x-1)-(x+1)/(x-1)2=3(x+1)2/(x-1)2·-2/(x-1)2=-6(x+1)2/(x-1)4.

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