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What is the second derivative of xsqaured e to the power of x?
Elaine23
f(x) = (x^2)(e^x)
f'(x) = e^x((x^2)+2x) - i think
f"(x) = ?
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f(x) = (x^2)(e^x)
apply the power rule
f'(x) = (x^2)(e^x) + (2x)(e^x)
apply the power rule to the first part and apply the power rule to the second part, then add those together
f''(x) = [(x^2)(e^x) + (2x)(e^x)] + [(2x)(e^x) + (2)(e^x)]
simplify
f''(x) = (e^x)(x^2 + 4x +2)
I got it right. It checked out on my calculator.
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