Question

Find f '(x) and f ''(x).
f(x)= x/9-e^x

Answer 1

really having an issue with differentiables containing square roots and e^x

Answer 2

the derivative of e^x is always e^x, forever, it's its own derivative

Answer 3

what if a number is attached like the 9-e^x?

Answer 4

derivativave of 9 is 0,

Answer 5

ahh so you do seperate it... the derivative of 9 then e^x

Answer 6

So, 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)

Answer 7

right

Answer 8

So 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.

Answer 9

\[(x(e ^{x}))-(1(9+e^{x}))/(9+e^{x})^{2}\]

Answer 10

Is that a different problem?

Answer 11

its not subtract its divide

Answer 12

x divided by 9+e^{x}

Answer 13

Ah, got it.

Answer 14

So:

\[f(x) = \frac{x}{9 + e^x}\]?

Answer 15

yes and the other was the answer i got

Answer 16

I've always found it easiest to use product rule when I have division like that.

In this case, you're looking at:

\[f(x) = x(x + e^x)^{-1}\]

Answer 17

So 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)

Answer 18

and thats the answer to fprime?

Answer 19

sorry 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

Answer 20

what is wrong with the answer i found?

Answer 21

Sorry, browser retardedness.

Answer 22

i feel ya

Answer 23

Also, what I meant was that you're looking at :

\[f(x) = x(9 + e^x)^{-1}\]

Answer 24

Looks like the only issue you had was a sign issue.

Answer 25

I ultimately got:

\[\frac{9 + e^x - xe^x}{(9 + e^x)^2}\]