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Find y' and y" if y = x^4*e^x

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sllysmith | Student, Undergraduate | (Level 2) eNoter

Posted March 21, 2012 at 10:22 AM via web

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Find y' and y" if y = x^4*e^x

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 21, 2012 at 10:50 AM (Answer #1)

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It is given that y = x^4*e^x

To find the derivatives use the product rule.

y' = 4x^3*e^x + x^4*e^x

=> (x^4 + 4x^3)*e^x

y'' = 12x^2*e^x + 4x^3*e^x + 4*x^3*e^x + x^4*e^x

=> (x^4 + 8x^3 + 12x^2)*e^x

The derivative y' = (x^4 + 4x^3)*e^x and y'' = (x^4 + 8x^3 + 12x^2)*e^x

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