Maclaurin Series xe^x
The Maclaurin series expansion for xe^x is very easy to derive. This is one of the easiest ones to do because the derivatives are very easy to find. All you have to do is to find the derivatives, and their values when x = 0. Then substitute them into the general formula shown above.
When x = 0, xe^x = 0 because anything multiplied by 0 is 0.
The value of the first derivative of xe^x is 1
This is the second derivative for xe^x
This is the third derivative
This is the fourth derivative
This is an easy pattern to figure out.
Just substitute the values into the general formula.
This is the Maclaurin series for xe^x.