Question

Differentiate 17xe^-x

Answer 1

\[f(x)=17xe ^{-x}\]

Answer 2

I really only know how to use the power rule and can tell that's what i'm suposed to use here. I"m just confused because there are three terms there, not just two (aka 17, x, e^-x)

Answer 3

Hey There! Sounds like Calculus. The Power rule is that you bring the power to the front of the equation and subtract the exponent by one. So think of 17x as \[17x^1 \]

Answer 4

i meant product rule, sorry

Answer 5

Oh Product

Answer 6

i do also know the power rule though

Answer 7

When you think of the product rule, You realize that you have 2 functions in front of you correct?

Answer 8

don't i have three? 17, x, and e^-x?

Answer 9

or should i think of them as 17x and e^-x?

Answer 10

Yep :) When you see that x, think of the number in front of it. You never treat a number away from the x.

Answer 11

would i do : \[17x(e ^{-x})+ e ^{-x}(17)\]

Answer 12

Actually it is \[17* (-e)^x\]

Answer 13

17x that is.

Answer 14

well an example problem using 15 instread of 17 shows it as \[-15x(e ^{-x})+e ^{-x}(15)\]

Answer 15

why is that 15 out front negative?

Answer 16

You see how it is \[e^-x\]?

Answer 17

Well, e^-x?

Answer 18

yes, in the original function it is

Answer 19

Yep! The negative is going to come from that -x. e is a weird rule that when you take the derivative of it, you are merely multiplying that 17x by -1.

Answer 20

Does that make sense? I hope I haven't lost you :(

Answer 21

but i thought the derivate of e^x was always e^x, not 1

Answer 22

Think of e^x as e^(1)x. This will make your life a lot easier.

Answer 23

I"m gonna attach a screen shot of the whole problem that I am given and the example worked out. It is just using 15, instead of 17. Maybe you can help clarify that for me

Answer 24

ok, so what does that do for me? Wouldn't the negative just follow in the rule? aka e^-1x derivatie is e^-1x?

Answer 25

Nope. You are going to bring that -1 Down to in-front of the equation. I'm not sure how your teacher taught it but my Calculus teacher informed of that rule because I was in your shoes about 2 months ago. She explained to me as if there are imaginary ones. I.e\[1e ^{-1x}\]

She then said, That 1 wants to be just like that -1 So it is going to convert to that, as if it were the newest technology. So your answer would be

\[-1e ^{-1x}\].


Does that clear it up any better?

Answer 26

oh, ok that's good to know. My teacher never mentioned that

Answer 27

Thanks, that does help. I don't need to really work it out any more than that to go ahead and get the second derivative, do i?

Answer 28

i"ll just have to do the product rule twice and add them together. I think

Answer 29

You only have to do the product rule, so the First (17x) multipled by the derivative of the second, + the second times the derivative of the first.

Answer 30

Depending on your teacher, you might have to. My teacher just tells us to do it once and your done!

Answer 31

Yeah, i did that a few posts up

Answer 32

well i'm suposed to do it again, but your little rule helps. so thanks!

Answer 33

No problem :) any questions just ask away! BC Calc Woop Woop.