Find the first and second derivatives of the function.y=xe^(7x) .......y= xe to the (7x) power y'=____ y''=___

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

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`y= xe^(7x)`

Use the product rule.

`==gt y'= (x)'(e^(7x)) + (x)(e^(7x))' `

`==gt y' = e^(7x) + x(7e^(7x)) `

`==gt y'= e^(7x) ( 1+ 7x)`

Now we will find the second derivative.

Also, we will use the product rule.

`==gt y''= (e^(7x))'(1+7x)+ (e^(7x))(1+ 7x)' `

`==gt y''= 7e^(7x)(1+7x) + 7e^(7x) `

`==gt y''= 7e^(7x) (1+ 7x + 1) `

`==gt y''= 7e^(7x) (7x+2)`

 

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