Find the 100th derivative of xe^x

Expert Answers
justaguide eNotes educator| Certified Educator

The function f(x) = x*e^x

The first derivative f'(x) = x*(e^x)' + x'*e^x

=> x*e^x + e^x

The second derivative is x*e^x + e^x + e^x = x*e^x + 2*e^x

As higher derivatives follow a similar pattern, the 100th derivative is x*e^x + 100*e^x

The 100th derivative of f(x) = x*e^x is x*e^x + 100*e^x