Question

I need help on this question!!!
f(x)=(e^x)/(e^x+2)(x+3)
find the derivative f'(x)=_____
Please help me!!

Answer 1

It's hard to read it properly with the way you formatted it.
Is this correct?\[\Large f(x)\quad=\quad \frac{e^x}{(e^x+2)(x+3)}\]

Answer 2

that is correct!

Answer 3

\[\Large f'(x)=\frac{\color{royalblue}{\left[e^x\right]'}(e^x+2)(x+3)-e^x\color{royalblue}{\left[(e^x+2)(x+3)\right]'}}{\left[(e^x+2)(x+3)\right]^2}\]

Answer 4

Oh boy this is going to be a doozy.
So there is our quotient rule setup.
We'll need to take the derivatives of the blue portions.

Answer 5

Looks like we'll need to apply the product rule to the second blue part.
Any confusion on the quotient rule setup? :o

Answer 6

no I am pretty comfortable with the quotient rule

Answer 7

jealous !! he makes the explanation clear with color.

Answer 8

i have the correct set up, for some reason i am not carrying my math out right

Answer 9

nice use of \(\color{blue}{color}\)

Answer 10

i still do not understand even with the color can someone explain it to me please haha

Answer 11

Ah sorry I ran off for a sec there :d

Answer 12

So what does the derivative of the first blue part give you?
e^x comes out of that one, right? :o

Answer 13

\[\Large f'(x)=\frac{\color{orangered}{\left[e^x\right]}(e^x+2)(x+3)-e^x\color{royalblue}{\left[(e^x+2)(x+3)\right]'}}{\left[(e^x+2)(x+3)\right]^2}\]

Answer 14

i believe that is correct

Answer 15

So I guess the tricky part is the other blue part,
product rule time!\[\Large \left[(e^x+2)(x+3)\right]'=\color{teal}{\left(e^x+2\right)'}(x+3)+(e^x+2)\color{teal}{\left(x+3\right)'}\]

Answer 16

hmm would that be e^x(x+3) + (e^x +2)(1)

Answer 17

Mmmmm yah looks good!

Answer 18

\[\Large f'(x)=\frac{\color{orangered}{\left[e^x\right]}(e^x+2)(x+3)-e^x\color{orangered}{\left[e^x(x+3)+(e^x+2)\right]}}{\left[(e^x+2)(x+3)\right]^2}\]

Answer 19

So from thereeeeee, it's just some... messy... simplification :\

Answer 20

imma go make a sammich, simplifyyyy \c:/

Answer 21

haha alright so the squared on the bottom gets cancelled because of the ones in the numerator

Answer 22

The square? yah that sounds right, leaving us with a 1 exponent down there.

Answer 23

Err wait wait :p

Answer 24

We don't have an \(\Large (e^x+2)(x+3)\) in the second term :( Hmm

Answer 25

right then it would be -e^x/ (e^x+2)(x+3)

Answer 26

would it?

Answer 27

how could i simplify this further??

Answer 28

I dunnoooo :( too much multiplication.. brain.. hurts.

Answer 29

is the answer this -e^x/ (e^x+2)(x+3) because i plugged that in and i was told it was wrong

Answer 30

haha believe me my brain hurts too i have been on this problem for the last two hours

Answer 31

bahh i dunno +_+ ill multiply it out after i finish this slice of pizza

Answer 32

thank you so much i really appreciate it!

Answer 33

Mmm it looks like this is not going to simplify nicely, you should try to put it all into your answer. :\

Answer 34

I'm not sure how you got (e^x+2)(x+3) in your denominator... Hmm

Answer 35

good point im not sure either haha im so confused with this problem i understand the rules but for some reason this problem is getting to me

Answer 36

you are an absolute genius thank you so very much!! you saved me big time!!!!!!!!