The question is take the derivative of this:
f(x) = (x^2 + 2x +3)e^-x
I got f'(x) = (2x+2)(e^-x) + (x^2 + 2x +3)(e^-x)'
I know that the derivative of e^x is e^x but what about e^-x?
I thought that it was maybe (-1)(e^-x)
So when I simplified, I got
(-1)(x^2 + 1)(e^-x) but, this was wrong, and I can't figure out why....
2007-07-25 19:10:43 · 4 answers · asked by ahelaumakani 4 in Science & Mathematics ➔ Mathematics
It's wrong because my class uses an online homework server for inputting answers. When I put my answer in, it was wrong. :(
2007-07-25 19:19:42 · update #1
f (x) = (x² + 2x + 3) e^(-x)
f `(x) = (2x + 2)e^(-x) - e^(-x) (x ² + 2x + 3)
f `(x) = e^(-x)[ 2x + 2 - x ² - 2x - 3 ]
f `(x) = - e^(-x) [ 1 + x ² ]
Which is the same as your answer---surely we both can`t be wrong!
2007-07-25 22:31:24 · answer #1 · answered by Como 7 · 0⤊ 0⤋
f(x) = (x^2)(e^-x) + 2x(e^-x) + 3e^-x
f'(x) = 2x(e^-x) - x^2(e^-x) + 2(e^-x) - 2x(e^-x) - 3(e^-x)
f'(x) = e^-x [ -x^2 - 1]
your answer is correct.
2007-07-25 19:19:31 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Your work all looks good to me. What makes you think that it is wrong?
2007-07-25 19:16:39 · answer #3 · answered by Grumpy 2 · 0⤊ 0⤋
Your analysis is correct.
d/dx (e^-x) = -e^(-x)
and your simplified answer is correct.
The online server is wrong.
2007-07-25 19:19:20 · answer #4 · answered by ? 3 · 0⤊ 0⤋