Engineering Board Exam Reviewer · Derivatives of Algebraic Functions · hard

Find y' if y=(x2-3)4(2x+1)2.

1. 4(x2-3)3(2x+1)(5x2+2x-3)
2. 8x(x2-3)3(2x+1)2
3. 4(x2-3)4(2x+1)
4. (x2-3)3(2x+1)(5x2+2x-3)

Answer

A. 4(x2-3)3(2x+1)(5x2+2x-3)

Solution

By the product rule with u=(x2-3)4, v=(2x+1)2: u'=8x(x2-3)3, v'=4(2x+1). Then y'=8x(x2-3)3(2x+1)2+4(2x+1)(x2-3)4, which factors to 4(x2-3)3(2x+1)(5x2+2x-3).

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