AP Calculus ABeasymcq1 pt
If f(x) = x²eˣ, what is f'(x)?
A.2xeˣ
B.x²eˣ
C.eˣ(x² + 2x)
D.eˣ(x² - 2x)
Explanation
Core Concept
This requires the product rule for differentiation. Let u = x² and v = eˣ. Then f'(x) = u'v + uv' = (2x)(eˣ) + (x²)(eˣ) = eˣ(2x + x²) = eˣ(x² + 2x).
Correct Answer
Ceˣ(x² + 2x)
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