How do you differentiate #g(x) =(2x+2)e^(3-x) # using the product rule?

1 Answer
Shwetank Mauria
Mar 12, 2018

Derivatie of #g(x)=(2x+2)e^(3-x)# is #-2xe^(3-x)#

Explanation:

Product rule states that derivative of a product of two functions is equal to first function multiplied by derivative of second function plus second function multiplied by derivative of first function.

Here #g(x)=(2x+2)e^(3-x)# and while first function is #2x+2#, whosederivative is #2#, second function is #e^(3-x)# and its derivative is #-e^(3-x)#.

and therefore #(dg)/(dx)=2xxe^(3-x)+(2x+2)(-e^(3-x))#

= #e^(3-x)(2-2x-2)#

= #-2xe^(3-x)#

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