How Do You Apply the Product Rule to Differentiate uxe^-x?

In summary, the method to differentiate uxe^-x for a reduction order question is to use the general rule (ABC)' = A'BC + AB'C + ABC' and treat ux as a single unit instead of u and xe^-x separately. This results in -uxe^-x + ue^-x as the final answer. Any further assistance can be sought from the Physics Forums community.
  • #1
jackalope1234
9
0

Homework Statement


I need to differentiate uxe^-x in order to do a reduction order question.


Homework Equations


d/dxf(x)g(x) = f(x)g'(x) + g(x)f'(x) <--- that's the product rule about 2 variable


The Attempt at a Solution


I would assume
y' = -uxe^-x + u'xe^-x

I was told elsewhere you would consider the ux as a single unit as opposed to the u and xe^-x though resulting in
-uxe^-x + ue^-x

any help would be appreciated.
 
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  • #2
welcome to pf!

hi jackalope1234! welcome to pf! :wink:

general rule: (ABC)' = A'BC + AB'C + ABC' :smile:

(because it's (AB)'C + (AB)C')
 
  • #3
I assumed "general rule: (ABC)' = A'BC + AB'C + ABC' " would be the method thank you for confirming. thank you for the welcome, maybe this forum will pull me away from starcraft 2 :D.
 

FAQ: How Do You Apply the Product Rule to Differentiate uxe^-x?

What is the purpose of differentiating uxe^-x?

The purpose of differentiating uxe^-x is to find the derivative of the function, which tells us how the function changes with respect to its independent variable. In other words, it helps us understand the rate of change of the function at any given point.

What is the general rule for differentiating uxe^-x?

The general rule for differentiating uxe^-x is to first identify the function inside the parentheses (ux), then multiply it by the derivative of the exponent (-x), and finally add the derivative of the function (u) multiplied by the exponent (e^-x).

How do you differentiate a function with a product using the chain rule?

To differentiate a function with a product using the chain rule, you first differentiate the outer function and then multiply it by the derivative of the inner function. This can be remembered using the acronym "UDU" (u times derivative of u).

What is the purpose of simplifying the final derivative?

The purpose of simplifying the final derivative is to make the expression cleaner and easier to work with. It also helps us identify patterns and relationships that can be useful in further calculations or applications of the derivative.

Can the process of differentiating uxe^-x be applied to other functions?

Yes, the process of differentiating uxe^-x can be applied to other functions that follow the same general rule of identifying the function inside the parentheses, multiplying it by the derivative of the exponent, and adding the derivative of the function multiplied by the exponent. However, for more complex functions, additional rules and techniques may be necessary.

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