AP Calculus ABeasymcq1 pt
If f(x) = x²e^x, what is f'(x)?
A.B) x²e^x
B.C) e^x(x² + 2x)
C.D) e^x(x² - 2x)
D.A) 2xe^x
Explanation
Core Concept
This requires the product rule for differentiation. Let u = x² and v = e^x. Then f'(x) = u'v + uv' = (2x)(e^x) + (x²)(e^x) = e^x(2x + x²) = e^x(x² + 2x).
Correct Answer
BC) e^x(x² + 2x)
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