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Help!! I am terrible at problems like this:

 

Suppose that f(x)= x+7/e^x

 

Find f ' (2)

 Feb 19, 2016
 #1
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I assume that this is :

 

f(x)= (x+7)/e^x      note that this can be written as :

 

f (x)   =  ( x  + 7) * e^(-x)     so..........we can use the Product Rule to find the derivative

 

f ' (x)  = (1) * e^(-x)   + ( x + 7) * ( - 1)e^(-x)  =     e^(-x) [ 1 - ( x + 7) ] =  e^(-x) ( -x - 6)  =

 

-e^(-x) ( x + 6)

 

So

 

f ' (2)  =  -e^(-2)(2 + 6)  =  - [ 8 ] / [ e^2 ]   =  about  - 1.08268

 

 

cool cool cool

 Feb 19, 2016
 #2
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Thank ya!

 Feb 19, 2016

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