Question

First derivative with steps:

1+(2+x)(e^(x/3))

Answer 1

looks like you need to use the product rule mixed with the quotient rule. Are you familiar with either of these?

Answer 2

Yes, I already came up with an answer, but I don't think it is right. I need steps done so I can compare them with mine and find the mistake.

Answer 3

post ur answer

Answer 4

Ok give me just a second

Answer 5

1/3(e^(x/3))(x+5)

Answer 6

\[1+(2+x)(e^{(x/3)})\]\[(2+x)e^{x/3}\frac{1}{3}+x^{x/3}\]

Answer 7

\[y=uv\]\[y'=uv'+u'v\]

Answer 8

So is that the answer orate hose steps?

Answer 9

*or are those

Answer 10

answer. Not that much steps involved.

derivative of (x+2) is 1

derivative of 1 is 0

derivative of e^(x/3) is [e^(x/3)] (1/3)

Answer 11

so just apply the product rule

Answer 12

And you are absolutely positive?

Answer 13

yup

Answer 14

Ok thank you

Answer 15

do you think that you would distribute the e^x/3 first before taking the derivative?

Answer 16

@Hero double check my sol'n plz

Answer 17

wolfram alpha matches with your answer

Answer 18

I'm not sure, that's why I asked the question

Answer 19

I'm going to simplify mine and maybe i'll get urs. hold on plz

Answer 20

\[(2+x)e^{x/3}\frac{1}{3}+x^{x/3}\]\[\frac{2}{3}e^{x/3}+(1/3)xe^{x/3}+e^{x/3}\]\[e^{x/3}(\frac{5}{3}+(1/3)x)\]\[\frac{1}{3}e^{x/3}(5+x)\]Ya same answer. Sorry if that confused you

Answer 21

correction on first line: last term should be e^(x/3)