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`f(x)=( 3x^2+1) / (e^(2x))` Find the derivative.

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good2beme | Student, Undergraduate | (Level 1) Honors

Posted June 20, 2012 at 2:59 AM via web

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`f(x)=( 3x^2+1) / (e^(2x))`

Find the derivative.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted June 20, 2012 at 3:13 AM (Answer #1)

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`f(x)= (3x^2+1)/(e^(2x))`

To find the derivative, we will use the qoutient rule.

 

`==gt If f(x)= u/v `

`==gt f'(x)= (u'v-uv')/(v^2) `

`==gt f'(x)=( (3x^2+1)'(e^(2x)) - (3x^2+1)(e^(2x))')/(e^(2x))^2`

 

`==> f'(x) = ((6x(e^(2x))- (3x^2+1)(2e^(2x)))/(e^(4x)))`

`==> f'(x)= (6xe^(2x) - 6x^2 e^(2x) - 2e^(2x))/(e^(4x))`

`==> f'(x)= (2e^(2x) ( 3x - 3x^2 -1))/(e^(4x))`

`==> f'(x) = (-2(3x^2-3x+1))/(e^(2x))`

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