Question

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

Answer 1

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)`