Differentiation (Single-Variable Calculus)
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Differentiate \(y=x^2e^{3x}\).
Product-and-chain structure
Required reasoning
\(u=x^2\), \(v=e^{3x}\)
Use \((uv)'=u'v+uv'\)
Select the exact answer.
Select one option.
A
\(3x^2e^{3x}\)
B
\(e^{3x}(2+3x)\)
C
\(x^2e^{3x}\)
D
\(e^{3x}(2x+3x^2)\)
E
\(2xe^{3x}\)
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