# Product rule calculus help

y = x ln x

$$\frac{dy}{dx} = \frac{1}{x ln x} \cdot 1$$

Is that correct?

wrong... use product rule

$$\frac{d}{dx} (fg) = \frac{df}{dx}g+f\frac{dg}{dx}$$

And how would that look like? Which is f & which one is g? Hmm i'm not great at this but,

y = x lnx
I was gunna say.. that whenever you take the derivative of logs.. 1/function * derivative of that function
so that'd give you
y = (1/xlnx)(1/x)
but by using the product rule...
y = 1(xlnx) + x(1/x))
Hmm, definately don't listen to me, i don't know WHats going on. Here to learn!

SphericalStrife said:
Hmm i'm not great at this but,

y = x lnx
I was gunna say.. that whenever you take the derivative of logs.. 1/function * derivative of that function
so that'd give you
y = (1/xlnx)(1/x)
I was taught that way. How did you get 1/x?

hmm I think i might just be being stupid. 1/x is the known derivative of lnx.. but i guess with that other x there.. x lnx, you would need to use product rule like that guy said?

Oh I see...
SphericalStrife said:
1/x is the known derivative of lnx
How do you know it?

Use product rule. f(x)=x and g(x)=ln(x)
Now just find derivatives
y = x'*lnx + x*ln(x)'

Yeah I got it. Thank you.
{"ft_lang_label":"__label__en","ft_lang_prob":0.89052355,"math_prob":0.98913634,"size":489,"snap":"2021-31-2021-39","text_gpt3_token_len":174,"char_repetition_ratio":0.12577319,"word_repetition_ratio":0.13953489,"special_character_ratio":0.34560326,"punctuation_ratio":0.10526316,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9982756,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-23T00:51:30Z\",\"WARC-Record-ID\":\"<urn:uuid:a6c08838-39fd-49dc-a3ed-6eee948d29ef>\",\"Content-Length\":\"77595\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9ac9f0f0-ebaf-463c-8c85-cc37cbf370c5>\",\"WARC-Concurrent-To\":\"<urn:uuid:7622640b-9df0-42de-9735-4c7e5afa2243>\",\"WARC-IP-Address\":\"104.26.14.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/product-rule-calculus-help.66002/\",\"WARC-Payload-Digest\":\"sha1:LVT3AO6GW7M6ANMPHEDXEP7PQ2UERPFW\",\"WARC-Block-Digest\":\"sha1:L5B7U43OFICSMMXI7FLDCJIVZSY63WEE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057403.84_warc_CC-MAIN-20210922223752-20210923013752-00650.warc.gz\"}"}