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anonymous
 5 years ago
Find f '(x) and f ''(x).
f(x)= x/9e^x
anonymous
 5 years ago
Find f '(x) and f ''(x). f(x)= x/9e^x

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0really having an issue with differentiables containing square roots and e^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the derivative of e^x is always e^x, forever, it's its own derivative

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what if a number is attached like the 9e^x?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0derivativave of 9 is 0,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahh so you do seperate it... the derivative of 9 then e^x

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So, when you take a derivative, you always take the separate derivative of parts that are added or subtracted together. For example: f(x) = g(x) + h(x) f'(x) = g'(x) + h'(x) f''(x) = g''(x) + h''(x) And: f(x) = g(x)  h(x) f'(x) = g'(x)  h'(x) f''(x) = g''(x)  h''(x)

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So let's take your problem in particular: \[f(x) = \frac{x}{9}  e^x\] You have to first take the derivative of \(\frac{x}{9}\), then that of \(e^x\). Then, you can subtract the latter from the former.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(x(e ^{x}))(1(9+e^{x}))/(9+e^{x})^{2}\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Is that a different problem?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its not subtract its divide

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So: \[f(x) = \frac{x}{9 + e^x}\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes and the other was the answer i got

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0I've always found it easiest to use product rule when I have division like that. In this case, you're looking at: \[f(x) = x(x + e^x)^{1}\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So in this case, we have product rule. Product rule says: f(x) = h(x)g(x) f'(x) = h'(x)g(x) + h(x)g'(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and thats the answer to fprime?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry to be the pain! lol im a non traditional student that never took calc in high school sad thing is im trying to major in it lmao

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is wrong with the answer i found?

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, browser retardedness.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Also, what I meant was that you're looking at : \[f(x) = x(9 + e^x)^{1}\]

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0Looks like the only issue you had was a sign issue.

shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0I ultimately got: \[\frac{9 + e^x  xe^x}{(9 + e^x)^2}\]
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