Maclaurin Series xe^x

expansion

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.

xe^x

When x = 0, xe^x = 0 because anything multiplied by 0 is 0.

First Derivative

The value of the first derivative of xe^x is 1

Second Derivative

This is the second derivative for xe^x

Third Derivative

This is the third derivative

Fourth Derivative

This is the fourth derivative

Pattern

This is an easy pattern to figure out.

Substitution

Just substitute the values into the general formula.

Maclaurin series for xe^x

This is the Maclaurin series for xe^x.