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What is the derivative of y = x^2*e^(4x)

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rajdarshani | Student, Grade 11 | Salutatorian

Posted June 12, 2012 at 1:01 AM via web

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What is the derivative of y = x^2*e^(4x)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 12, 2012 at 2:35 AM (Answer #1)

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The function `y = x^2*e^(4x)` . The derivative can be found using the product rule.

`y' = (x^2)'*e^(4x) + x^2*(e^(4x))'`

=> `2*x*e^(4x) + x^2*4*e^(4x)`

=> `2*x*e^(4x)(1 + 2x)`

The derivative of `y = x^2*e^(4x)` is `y' = 2xe^(4x)(1 + 2x)`

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