SOLUTION: Use the Maclaurin series of f(x) = e^x to verify that d/dx e^x = e^x. Thank you!

Algebra ->  Sequences-and-series -> SOLUTION: Use the Maclaurin series of f(x) = e^x to verify that d/dx e^x = e^x. Thank you!      Log On


   

Question 578370: Use the Maclaurin series of f(x) = e^x to verify that d/dx e^x = e^x.
Thank you!
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
the Maclaurin series of f(x) = e^x
e%5Ex=1%2Bx%2Bx%5E2%2F2%21%2Bx%5E3%2F3%21%2Bx%5E4%2F4%21+...
then d/dx e%5Ex =d/dx (1%2Bx%2Bx%5E2%2F2%21%2Bx%5E3%2F3%21%2Bx%5E4%2F4%21+...)=0%2B1%2B2x%2F2%21%2B3x%5E2%2F3%21%2B4x%5E3%2F3%21+...=1%2Bx%2Bx%5E2%2F2%21%2Bx%5E3%2F3%21+...=e%5Ex