# How do you find #f^6(0)# where #f(x)=xe^x#?

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Or:

The following yields a general Maclaurin series:

calculating the coefficients of each:

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To find ( f^6(0) ) where ( f(x) = xe^x ), you would:

- Calculate the first derivative of ( f(x) ) with respect to ( x ).
- Then, calculate the second derivative of ( f(x) ).
- Repeat this process until you've calculated the sixth derivative of ( f(x) ).
- Evaluate the sixth derivative of ( f(x) ) at ( x = 0 ) to find ( f^6(0) ).

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