Engineering Board Exam Reviewer · Derivatives of Algebraic Functions · hard

Find y' if y=x2sqrt(x+1).

1. 5x2+4x2sqrt(x+1)
2. 2xsqrt(x+1)
3. x22sqrt(x+1)
4. 5x2+4xsqrt(x+1)

Answer

A. 5x2+4x2sqrt(x+1)

Solution

By the product rule: y'=2xsqrt(x+1)+x2· 12sqrt(x+1). Combining over a common denominator: y'= 4x(x+1)+x22sqrt(x+1)= 5x2+4x2sqrt(x+1).

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