Expert: Steve Holleran - 4/16/2008

Question
I don't understand the whole d/dx when finding the differation of a simple exponent such as

y = (x^2)(e^2x)

Could you explain what you are doing, I have asked other people and they just give me the answer.  I really appreciate it.   Thanks

Answer
Hello Matt,

To find a derivative when you have one function multiplying another, you have to use a process called the Product Rule.

Basically, it says you should multiply each function by the derivative of the other, and add the results:

       (fg)' = f' * g + g' * f

So, here we have

       (x^2 * e^2x)' = (x^2)' * (e^2x) + (e^2x)' * (x^2)

                     =  2x * e^2x   +   2e^2x * x^2.

Many texts will pull common factors out and write the answer like this:

                    = 2x e^2x (1 + x).

I hope this helps you out.

Steve